For 0 2 find the values of the trigonometric functions based...

For 0 < θ < π/2, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as expressions, e.g. you can enter 3/5). If cos(θ) = 2/9 then sin(θ) = ? sec(θ) = ? csc(θ) = ? tan(θ) = ? cot(θ) = ?

Transcript

00:01 Okay, we are given some information and we are asked to find the remaining trigonometric functions.

00:08 So one bit of information that we're given is that theta is between zero and two, i'm sorry, not two, but pi over two.

00:16 So theta is between zero and pi over two.

00:20 So what that means, if i look at a cartesian plane, that means that i have to be here in quadrant one.

00:28 It's important to know that because as i go through and i'm figuring out what my trig functions are, i need to know are they positive or negative.

00:39 Well, in quadrant one, everything is positive.

00:42 So that's good to know.

00:44 Now, the other thing we're given is that cosine theta is equal to two nights.

00:50 So there's one.

00:51 We've got cosine theta right away.

00:53 So that also gives us secant theta, because secant is simply the reciprocal.

00:58 Of cosine, equal sign.

01:02 But that secant, because of cosine of theta is two nints, then the secant of theta is nine over two.

01:09 So there's a couple of ways that you can go about this.

01:12 I'm going to use a trig identity, because one identity i know is that cosine squared plus sine squared is equal to one.

01:24 So i already know what cosine is.

01:26 It's given to me right there.

01:28 So two nights squared.

01:31 Plus sine squared is equal to 1.

01:35 So this is going to be 4 over 81, and 1 is the same as 81 over 81.

01:48 So i'm going to subtract this 4 over 81, so that i have sine squared theta is equal to 81 minus 4 would be 77 over 81...

Question

For 0 < θ < π/2, find the values of the trigonometric functions based on the given one (give your answers with THREE DECIMAL PLACES or as expressions, e.g. you can enter 3/5). If cos(θ) = 2/9 then sin(θ) = ? sec(θ) = ? csc(θ) = ? tan(θ) = ? cot(θ) = ?

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