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Video: Reciprocal Identities

Alex Cutbill

Complete the following: cos 𝜃 = 1/οΌΏ. [A] sin 𝜃 [𝐵] sec 𝜃 [C] cot 𝜃 [𝐷] csc 𝜃

01:33

Video Transcript

Complete the following: cos πœƒ is equal to one over something. And we have four options: option A is sin πœƒ, 𝐡 is sec πœƒ, C is cot πœƒ, and 𝐷 is csc πœƒ.

Okay. So let’s give that unknown something a name; let’s call it π‘₯. So now we have cos πœƒ 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œƒ is equal to one. Dividing both sides by cos πœƒ, we get that π‘₯ is equal to one over cos πœƒ. But unfortunately that isn’t one of our options. We have either A sin πœƒ, B sec πœƒ, C cot πœƒ, or D csc πœƒ 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œƒ is defined to be one over sin πœƒ. Cot πœƒ is one over 10 πœƒ. And the one that’s useful to us is sec πœƒ is equal to one over cos πœƒ.

So π‘₯, which is one over cos πœƒ, can also be written as sec πœƒ. And if we look through our options, we’ll see that B is our answer.