# Thread: How to find Cos 75°

1. ## How to find Cos 75°

A question in my math sheet asks to find "Cos 75 °"

We're on the unit of Compound Angle Formulae too. I was just wondering is it simply pressing cos 75 on the calculator or do I have to apply anything else to it? Thanks!

2. That's one way.
Or you can use the unit circle (if you don't know what that is search it on google).

3. Pressing cos(75deg) on the calculator is the easiest way.

But that's not the way you're asked to do. You are asked to do it using trigonometry.
You are on compound angles formulae, so that is the way you are supposed to do.

cos(75deg)
= cos(30deg +45deg)
= cos(30deg)cos(45deg) -sin(30deg)sin(45deg)
= [(sqrt(3) /2)*(1 / sqrt(2))] -(1/2)(1 / sqrt(2))
= [sqrt(3) / 2sqrt(2)] -[1 / 2sqrt(2)]
= [sqrt(3) -1] / [2sqrt(2)]

= [sqrt(6) -sqrt(2)] / 4

4. Thank you SOOO MUCH!

It makes sense now ^_^ You are all amazing!

What would you do for

Sin 15° since you can't split it into special angles?

Also, how do you simplify this:

sin (Θ + 30°) + cos (Θ + 60°)

5. Originally Posted by finalfantasy
Thank you SOOO MUCH!

It makes sense now ^_^ You are all amazing!

What would you do for

Sin 15° since you can't split it into special angles?

Also, how do you simplify this:

sin (Θ + 30°) + cos (Θ + 60°)
sin(15deg) = sin(45deg -30deg)

To simplify, spread them, simplify them.

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# without using the trigonometric table.find cos 75

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