Question

If cos Θ = -5/2 and tan Θ > 0, what is the value of sin Θ?

Explain bby

Answer 1

@iPwnBunnies

Answer 2

I ovb. know basic trig, but I don't understand wtf these types of questions are talking about

Answer 3

\(\tan\theta = \frac{\sin\theta}{cos\theta}\)

So if \(\tan\theta > 0\) then \(\sin\theta < 0\) because \(\cos\theta\) is negative.

Answer 4

I mean, I know how to solve it by the steps and rules given. sin Θ = (-√21)/5

But I like to see math visually... I don't get it.

Answer 5

Obviously, we're dealing with a right triangle. Also, you can think of the right triangle as being in the 3rd Quadrant of a coordinate plane. In Q3, tangent is positive, cos and sin are negative.

Answer 6

Ok hold on. I'll draw.

Answer 7

I get it bunnies don't draw it xD

Answer 8

Sweet. Yeah, so find the reminaing leg of the pseudo triangle, and find the sine.

Answer 9

You might wanna remember this.

All Students Take Calculus. All trig functions positive in Q1, sin positive in Q2, tan in Q3, cos in Q4. And their reciprocal counterparts.

Answer 10

But I just don't "see" it you know? I see mathematics (particularly mathamatical models) as common sense. In this situation, I just know the rules, not how to solve it individually. Why DF is the tangent positive while the Cosine and sine are negative in Q3.

Answer 11

I think of it like polar coordinates and regular coordinates.

Answer 12

BUNNIES I DON'T WANT TO REMEMBER IT xD I want to know the logic of it lol

Answer 13

The hypotenuse is like a polar line, extending to some (x,y) coordinate.

Answer 14

@Applesdaaasdasfdsfda if you look at my equation that I first stated, you'll see the mathematics behind why both cosine and sine are negative.

Answer 15

And you know that like, tan(x) = y/x, cos(x) = x/hyp
So, since y and x are both negative in Q3, tan would be positive. Everything else would be positive.

Answer 16

I should say the "mechanical" mathematics...

Answer 17

Yeah, dummyguy's thing works too. Two different ways to look at it.

Answer 18

Ohhhh I gettttchu. Thx bby ♥

P.S. Dummyguy, you too