# Thread: Need help on some Trig

1. ## Need help on some Trig

Having trouble with these problems can anyone help with any of these questions? And if possible can you explain> been working on this assignment all day and these are the only ones left.

Find the reference angle for the given angle.
1. 220
2. -225
3. 415

Use an addition or subtraction formula to write the expression as a trigonometric function of one number, and then find its exact value.

1. cos(80)cos(10)-sin(80)sin(10)
2. cos (7pie/6) cos (-pie/ 2)-sin(7pie/6)sine(-pie/2)
3. sin (255)
5. cot (135)
6. sin (5pie/6)

Find the exact value
tan(-195)
tan( -5pie/12)

2. A reference angle is the acute angle (<90) formed with the x-axis and the larger angle.
For example, a 220 degree angle can be represented by drawing a ray on the positive x-axis and a ray in the third quadrant. The ray in the third quadrant makes an acute angle of 40 with the x-axis. If you draw this out you should understand it pretty easily. The reference angle is always less than 90 degrees and it is between the x-axis and the second ray(the one not on the x-axis) in the larger angle.

Here are some of the formulas you need - your book should list the subtraction ones (or just let v be negative) - or search on wikipedia
sin(u+v) = cos(u)sin(v) + sin(u)cos(v)
cos(u+v) = cos(u)cos(v) - sin(u)sin(v)

Here is an example:
cos(u)cos(v)-sin(u)sin(v)=cos(u+v)
let u=80, let v=10
cos(u)cos(v)-sin(u)sin(v)=cos(80)cos(10)-sin(80)sin(10)=cos(80+10)=cos(90)=0

3. Thanks, but I'm still having trouble on

Use an addition or subtraction formula to find the exact value of the expression.
and

would I do it like

for sin (255) cos(135)sin(120) + sin(120)cos(135) then ? or ?

4. You wrote down the formula wrong, but I think you had the right idea

sin(255)=cos(135)sin(120) + sin(135)cos(120)

using the unit circle, sin(120) is the same as sin(60) which is 1/2
and sin(135) is the same as sin(45) which is (2^(1/2))/2
cos(135) is equal to -cos(45) so -(2^(1/2))/2
and cos(120) is -cos(60) so -(3^.5)/2

Again all of these values can either be read directly off of the unit circle. Depending of how the question is worded you probably could just say sin(120)=.5 etc.

After you sub. in the values just simplify it and you are done

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# simplify the equation cos(-60) tan 135Â°â„…tan 315Â° cos 660Â°

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