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Precalculus : Find the value of any of the six trigonometric functions

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Example Questions

Example Question #11 : Trigonometric Functions

Choose the answer which is equivalent to the following trig expression:

$Cos(\frac{3\pi}{2})$

Possible Answers:

$\frac{1}{2}$

Correct answer:

Explanation:

Choose the answer which is equivalent to the following trig expression:

$Cos(\frac{3\pi}{2})$

Begin by finding the location of our given angle. If we start at 0 on the unit circle and go clockwise, every quadrant covers $90^{\circ}/\frac{\pi}{2}$

Therefore, our given angle will correspond to $270^{\circ}$ , which is the bottom half of the y-axis.

Now, because cosine corresponds to the x-value, we know that this expression must be equivalent to 0. If we are on the y-axis, we have no x-value, and therefore, cosine must equal 0

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Example Question #12 : Trigonometric Functions

Which of the following is equivalent to the given expression?

$cot(\frac{3\pi}{2})$

Possible Answers:

Undefined

Correct answer:

Explanation:

Which of the following is equivalent to the given expression?

$cot(\frac{3\pi}{2})$

To simplify cotangent expressions, we can think of the expression as tangent and then simply take the reciprocal. So:

$tan(\frac{3\pi}{2})=\frac{1}{0}$ , which is undefined.

So,

$cot(\frac{3\pi}{2})=\frac{0}{1}=0$

Our answer is

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Example Question #13 : Trigonometric Functions

Simplify the following expression:

$\sec(-2\pi)$

Possible Answers:

Undefined

Correct answer:

Explanation:

Simplify the following expression:

$sec(-2\pi)$

I would begin here by recalling that secant is the reciprocal of cosine. Therefore, we can take the cosine of the given angle and then find its reciprocal.

So,

$cos(-2\pi)=1$

(Because cosine refers to x-values and $-2\pi$ lies on the x-axis)

Therefore,

$sec(-2\pi)=1$

Because $\frac{1}1{}=1$ .

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Example Question #14 : Trigonometric Functions

Calculate the value of the following trig function:

$sin270^{\circ}$

Possible Answers:

$\frac{\sqrt2}{2}$

Correct answer:

Explanation:

Calculate the value of the following trig function:

$sin270^{\circ}$

This is a problem which can be instantly solved by a calculator, provided it isn't in radian mode.

However, we are going to run through how to figure this out without a calculator, because knowing how to do it is far more powerful.

Begin by placing the angle in the unit circle. $270^{\circ}$ is a multiple of $90^{\circ}$ , more specifically, it is three times ninety.

Because we know our angle is three times ninety, we know the angle we are dealing with is one of our four "quadrantal" angles. These are the four that make up our x-y grid.

So, $270^{\circ}$ is the angle directly opposite of $90^{\circ}$ . This means our x-value must be zero, and our y-value must be .

Now, since we know that sine is basically our y-value, the value of $sin270^{\circ}$ must be equal to .

$sin270^{\circ}=-1$

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Example Question #15 : Trigonometric Functions

In a 3-4-5 right triangle, which of the following is a possible value for $sin(\theta)$ ?

Possible Answers:

$\frac{4}{3}$

$\frac{5}{3}$

$\frac{3}{5}$

$\frac{5}{4}$

$\frac{3}{4}$

Correct answer:

$\frac{3}{5}$

Explanation:

Sine theta is defined as the leg opposite to the angle over the hypothenuse. Write the definition of sine. The hypotenuse is the longest side of the right triangle, which indicates that 5 should be in the denominator.

$sin(\theta)= \frac{\textup{Opposite leg}}{\textup{Hypothenuse}}$

The ratio of the legs opposite to theta over the hypothenuse can either be $\frac{3}{5}$ or $\frac{4}{5}$ .

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Example Question #21 : Trigonometric Functions

Find the value of $\csc\theta$ .

$\theta=\frac{11\pi}{6}$

Possible Answers:

$\csc\theta=\frac{-1}{2}$

$\csc\theta=-2$

$\csc\theta=2$

$\csc\theta=\frac{2\sqrt3}{3}$

Correct answer:

$\csc\theta=-2$

Explanation:

Since

$\csc\theta=\frac{1}{\sin\theta}$

we begin by finding the value of $\sin\theta$ .

$\sin\frac{11\pi}{6}=-\frac{1}{2}$ .

Then,

$\csc\frac{11\pi}{6}=\frac{1}{-1/2}=-2$

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Example Question #11 : Find The Value Of Any Of The Six Trigonometric Functions

Determine the value of: $\cot(30^{\circ})$

Possible Answers:

$3\sqrt3$

$\frac{\sqrt3}{3}$

$\frac{\sqrt3}{4}$

$\sqrt3$

$\frac{\sqrt3}{2}$

Correct answer:

$\sqrt3$

Explanation:

To determine the value of cot(30) , simplify cotangent into sine and cosine.

$cot(30)=\frac{cos(30)}{sin(30)}= \frac{\frac{\sqrt3}{2}}{\frac{1}{2}}= {\frac{\sqrt3}{2}}\cdot{\frac{2}{1}}=\sqrt3$

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Example Question #13 : Find The Value Of Any Of The Six Trigonometric Functions

Find the value of $sec(\pi)+cos(-\pi)$ , if possible.

Possible Answers:

$\textup{The answer is not defined.}$

$\frac{\pi^2+1}{\pi}$

$\frac{1}{2}$

Correct answer:

Explanation:

In order to solve $sec(\pi)+cos(-\pi)$ , split up the expression into 2 parts.

$sec(\pi)= \frac{1}{cos(\pi)}=\frac{1}{-1}=-1$

$cos(-\pi)= -1$

$sec(\pi)+cos(-\pi)= -1-1=-2$

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Example Question #14 : Find The Value Of Any Of The Six Trigonometric Functions

Compute $\sec(300^\circ)$ , if possible.

Possible Answers:

$-\frac{1}{2}$

$\frac{1}{2}$

$\textup{The answer does not exist.}$

Correct answer:

Explanation:

Rewrite the expression in terms of cosine.

$sec(300)=\frac{1}{cos(300)}$

Evaluate the value of cos(300) , which is in the fourth quadrant.

$cos(300)= \frac{1}{2}$

Substitute it back to the simplified expression of sec(300) .

$sec(300)=\frac{1}{cos(300)}=\frac{1}{\frac{1}{2}}=2$

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Example Question #251 : Pre Calculus

Determine $csc(\frac{3\pi}{4})$

Possible Answers:

$\frac{2\sqrt 3}{3}$

$\frac{1}{\sqrt 2}$

$\sqrt 2$

Correct answer:

$\sqrt 2$

Explanation:

Remember that:

$csc(\frac{3\pi}{4})=\frac{1}{sin(\frac{3\pi}{4})}=\frac{1}{\frac{1}{\sqrt 2}}=\sqrt 2$

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Precalculus : Find the value of any of the six trigonometric functions

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #11 : Trigonometric Functions

Example Question #12 : Trigonometric Functions

Example Question #13 : Trigonometric Functions

Example Question #14 : Trigonometric Functions

Example Question #15 : Trigonometric Functions

Example Question #21 : Trigonometric Functions

Example Question #11 : Find The Value Of Any Of The Six Trigonometric Functions

Example Question #13 : Find The Value Of Any Of The Six Trigonometric Functions

Example Question #14 : Find The Value Of Any Of The Six Trigonometric Functions

Example Question #251 : Pre Calculus

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