Question

Evaluate lim θ→0 sin(cos 8θ)/sec 5θ.

Answer 1

The answer is 0.01745

Explanation:

Given the limit of the trigonometry function

lim θ→0 sin(cos 8θ)/sec 5θ

To evaluate the limit;

Step 1: substitute the value of θ =0 in the trigonometry function given to have;

lim θ→0 sin(cos 8θ)/sec 5θ

= sin(cos8(0))/sec5(0)

= sin(cos0)/sec0

Since cos 0= 1, the function becomes;

sin1/sec0

Step2: write the secant function as a function of cosine function where

Secθ = 1/cosθ

The resulting equation will become;

Sin1/(1/cos0)

Since cos0 = 1, the equation becomes;

Sin1/(1/1)

= sin1

= 0.01745

Answer 2

In this case, we are given with the expression sin(cos 8θ)/sec 5θ and is asked to evaluate the expression with limit as theta approaches 0. In this case, we just substitute 0 to theta. cos 0 is equal to 1 hence sec 0 is also equal to 1. sin theta is equal to 0.0175. Answer os 0.0175.