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Trigonometric identities assignment 4

Simplify 5 sin ø sec ø

A. 5 cot ø
B. 5
C. 5 cos ø
D. 5 tan ø

Trigonometric identities assignment 4 Simplify 5 sin ø sec ø A. 5 cot ø B. 5 C. 5 cos-example-1
User Khanou
by
8.2k points

2 Answers

1 vote

Answer:

D. 5 tan ø

Explanation:


5 \sin \phi \: \sec \phi \\ \\ = 5 \sin \phi \: * (1)/( \cos \phi) \\ \\ = 5 (\sin \phi)/( \cos \phi) \\ \\ = 5 \tan \phi

User Lachy
by
7.8k points
11 votes

Answer:

Correct choice D.

Explanation:

Trigonometric Identities

We need to recall some properties and definitions of the trigonometric functions.


\tan \theta=(\sin\theta)/(\cos\theta)


\sec \theta=(1)/(\cos\theta)

It's required to simplify the following expression:


5\sin\theta\sec\theta

Substituting the identity for the secant:


\displaystyle 5\sin\theta\sec\theta=5\sin\theta.(1)/(\cos\theta)

Operating:


\displaystyle 5\sin\theta\sec\theta=5(\sin\theta)/(\cos\theta)

Now we use the definition of the tangent:


\displaystyle 5\sin\theta\sec\theta=5\tan\theta

Correct choice D.

User Alejandro Colorado
by
8.7k points
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