Question Video: Using the Pythagorean Identities to Evaluate a Trigonometric Function | Nagwa Question Video: Using the Pythagorean Identities to Evaluate a Trigonometric Function | Nagwa

# Question Video: Using the Pythagorean Identities to Evaluate a Trigonometric Function Mathematics • First Year of Secondary School

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Find the value of cotΒ² π given cscΒ² π = 25/9.

01:39

### Video Transcript

Find the value of cot squared π given csc squared π is equal to 25 over nine.

Now what weβre absolutely not going to do is solve the equation csc squared π equals 25 over nine for π. Instead, weβre going to recall some trigonometric identities. The first identity we recall is that sin squared π plus cos squared π is equal to one. And weβre going to derive the next identity, though it is absolutely fine to simply quote it. Weβre going to divide each term here by sin squared π. sin squared π divided by sin squared π is equal to one. Then, we recall that cot π is equal to one over tan π. And tan π is sin π over cos π. So its reciprocal cot π must be equal to cos π over sin π.

This means that cos squared π over sin squared π must be equal to cot squared π. And then, since we know that csc π is equal to one over sin π, we can say that this is equal to csc squared π. Now, itβs absolutely fine to quote this identity one plus cot squared π equals csc squared π. To find an identity for cot squared π, Iβm going to subtract one from both sides. And we find that cot squared π is always equal to csc squared π minus one.

Now, in our question, weβre told that csc squared π is 25 over nine. So we can say that cot squared π here must be equal to 25 over nine minus one. To evaluate this, letβs write one as nine over nine. And when we subtract nine over nine from 25 over nine, we get 16 over nine.

And we find that when csc squared π is equal to 25 over nine, cot squared π is 16 over nine.

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