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Precalculus : Find the decimal value of a trigonometric function

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Example Questions

Example Question #1 : Evaluating Trig Functions

Find the value of cot(30)+tan(30) to the nearest tenth if sin(30)=0.5 and cos(30)= 0.866 .

Possible Answers:

2.3

2.9

3.2

1.7

Correct answer:

2.3

Explanation:

Rewrite cot(30)+tan(30) in terms of sine and cosine.

$cot(30)+tan(30)=\frac{cos(30)}{sin(30)}+\frac{sin(30)}{cos(30)}$

Substitute the known values and evaluate.

$\frac{0.866}{0.5}+\frac{0.5}{0.866}=1.732+0.577367 =2.309367$

The answer to the nearest tenth is 2.3 .

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Example Question #2 : Evaluating Trig Functions

Determine the value of $cot(\frac{\pi}{3})$ in decimal form.

Possible Answers:

-0.156

1.732

3.125

0.577

0.643

Correct answer:

0.577

Explanation:

Ensure the calculator is in radian mode since the expression shows the angle in terms of $\pi$ . Also convert cotangent to tangent.

$cot(\frac{\pi}{3})=\frac{1}{tan(\frac{\pi}{3})}= \frac{1}{\sqrt3}=0.577$

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Example Question #3 : Evaluating Trig Functions

Find the decimal value of

$2\cos\left(\frac{\pi}{6}\right)$

Possible Answers:

0.1542

1.732

0.5

0.3085

0.866

Correct answer:

1.732

Explanation:

To determine the decimal value of the following trig function, $2cos(\frac{\pi}{6})$ , make sure that the calculator is in radian mode.

Compute the expression.

$2cos(\frac{\pi}{6})=2(0.866)=1.732$

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Example Question #4 : Evaluating Trig Functions

Determine the correct value of

$sin\left(\frac{1}{2}^{\circ}\right)$ .

Possible Answers:

0.48

1.57

0.009

2.62

1.05

Correct answer:

0.009

Explanation:

The question $sin(\frac{1}{2})$ asks for the y-coordinate on the unit circle when the degree angle is $\frac{1}{2}$ .

Be careful not to confuse finding the value of the angle when the y-value of the coordinate of the unit circle is $\frac{1}{2}$ .

Ensure that the calculator is in degree mode.

$sin(\frac{1}{2})=0.00872=0.009$

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Example Question #5 : Evaluating Trig Functions

Find the value of

$\sin(270^\circ)+\cos(60^\circ)$ .

Possible Answers:

0.5

-0.5

1.13

1.5

-1.13

Correct answer:

-0.5

Explanation:

Before beginning this problem on a calculator, though this is not necessary since these are special angles, ensure that the mode of the calculator is in degrees.

Input the values of the expression and solve.

sin(270)+cos(60)= -1+0.5 = -0.5

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Precalculus : Find the decimal value of a trigonometric function

Study concepts, example questions & explanations for Precalculus

All Precalculus Resources

Example Questions

Example Question #1 : Evaluating Trig Functions

Example Question #2 : Evaluating Trig Functions

Example Question #3 : Evaluating Trig Functions

Example Question #4 : Evaluating Trig Functions

Example Question #5 : Evaluating Trig Functions

All Precalculus Resources

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