Question Video: Using Reciprocal Identities to Complete Trigonometric Expressions | Nagwa Question Video: Using Reciprocal Identities to Complete Trigonometric Expressions | Nagwa

# Question Video: Using Reciprocal Identities to Complete Trigonometric Expressions

Complete the following: cos π = 1/οΌΏ. [A] sin π [π΅] sec π [C] cot π [π·] csc π

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### Video Transcript

Complete the following: cos π is equal to one over something. And we have four options: option A is sin π, π΅ is sec π, C is cot π, and π· is csc π.

Okay. So letβs give that unknown something a name; letβs call it π₯. So now we have cos π is equal to one over π₯. And we want to find what π₯ is which means rearranging this equation for π₯.

So first we multiply both sides by π₯ to get π₯ cos π is equal to one. Dividing both sides by cos π, we get that π₯ is equal to one over cos π. But unfortunately that isnβt one of our options. We have either A sin π, B sec π, C cot π, or D csc π to choose from.

So at this point, we need to remember that the reciprocals of the trig functions sin, cos, and tan have other names. For example, csc π is defined to be one over sin π. Cot π is one over 10 π. And the one thatβs useful to us is sec π is equal to one over cos π.

So π₯, which is one over cos π, can also be written as sec π. And if we look through our options, weβll see that B is our answer.

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