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Trigonometry : Simplifying Trigonometric Functions

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Example Questions

Example Question #21 : Simplifying Trigonometric Functions

Which of the following is equivalent to

$\tan\theta\csc\theta$ ?

Possible Answers:

$\sin\theta$

$\tan\theta$

$\csc\theta$

$\sec\theta$

$\cos\theta$

Correct answer:

$\sec\theta$

Explanation:

In order to evaluate this expression, rewrite the trigonometric identity in terms of sines and cosines. The tangent is equal to the sine over the cosine and the cosecant is the reciprocal of the sine; thus, we can write the following:

$\tan(\theta)\csc(\theta)= \frac{\sin(\theta)}{\cos(\theta)}\times\frac{1}{\sin(\theta)}$

Now, can simplify. Notice that the sine terms cancel each other out.

$\frac{\sin(\theta)}{\cos(\theta)}\times\frac{1}{\sin(\theta)}= \frac{1}{\cos(\theta)}$

Remember, that the reciprocal of the cosine is the secant.

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

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Example Question #22 : Simplifying Trigonometric Functions

Change a $-240^{\circ}$ angle to radians.

Possible Answers:

2/3

$\frac{4\pi }{3}$

$4\pi$

$\frac{-4\pi }{3}$

Correct answer:

$\frac{-4\pi }{3}$

Explanation:

In order to change an angle into radians, you must multiply the angle by $\frac{\pi }{180^{\circ}}$ .

Therefore, to solve:

$-240^{\circ} \cdot \frac{\pi }{180^{\circ}} = \frac{-4\pi }{3}$

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Example Question #23 : Simplifying Trigonometric Functions

$\frac{\cos ^{2}x}{1+\sin x}$ The simple way to express this equation is:

Possible Answers:

$\small 1+\sin x$

$\small \tan x$

$\small 1-\sin x$

$\small 1$

$\small \sin x + \cos x$

Correct answer:

$\small 1-\sin x$

Explanation:

If $\sin ^{2}x+\cos ^{2}x=1$ , then $\cos ^{2}x=1-\sin ^{2}x$ . Place $\sin ^{2}x-1$ to $\cos ^{2}x$ . Then turn it to $\frac{(\sin x-1)*(\sin x+1)}{(\sin x-1)}$ . Get rid of $(\sin x-1)$ , and you will get $\sin x+1$ .

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Trigonometry : Simplifying Trigonometric Functions

Study concepts, example questions & explanations for Trigonometry

All Trigonometry Resources

Example Questions

Example Question #21 : Simplifying Trigonometric Functions

Example Question #22 : Simplifying Trigonometric Functions

Example Question #23 : Simplifying Trigonometric Functions

All Trigonometry Resources

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