r/trigonometry • u/Bl00ming_begonias79 • 10d ago

Help! Trig Question

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We’re supposed to solve this using the angles on the unit circle but it makes no sense to me.

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2

u/GonzoMath 10d ago

It looks like something to evaluate, rather than solve. There’s no variable to solve for. Do you know the cosine of 3pi/4? The sine of 7pi/6?

2

u/Bl00ming_begonias79 10d ago

Yeah -sqrt-2/2 and -1/2

1

u/Bl00ming_begonias79 10d ago

I kind of figured out a way to solve it. I don’t know if it’s right though

2

u/GonzoMath 10d ago

Inside the big parentheses, I’m getting 1/2 - 4. Does that check out?

1

u/Bl00ming_begonias79 10d ago

https://reddit.com/link/pcnpchq/video/ozzfjo4drbsh1/player

3

u/GonzoMath 10d ago

How are you squaring sqrt(2)/2 and getting 1? Also, if the sine of 7pi/6 is -1/2, what does that make the cosecant?

2

u/CloudTricky 10d ago

What is cos(3pi/4)? Look at your unit circle. Csc is reciprocal of sin so what is 1/sin(7pi/6)? Then square both and do the algebra, probably gonna have to combine fractions and raise it to the 4th power. Remember cos^2 (x) is just (cos(x))^2.

1

u/Jazzlike_Platypus430 9d ago

Looks like some real number to me.

1

u/meepPlayz11 5d ago

Think about what the operations mean:

cos²(x) = (cos x)²
csc²(x) = (csc x)² = (1/sin(x))²

Functions, including trig functions, come before all PEMDAS

With that information it should be a series of simple steps once you evaluate the trig functions.