What's the exact value of cos 135degrees and how dyu work it out? HELP!!?

Question

i know how to find exact values of 30, 45 and 60 degrees but not sure about obtuse angles.

Answer 1

it is -1/sqrt(2)

because cos(t) = - cos(180 -t) and t = 45 gives the result.

Answer 2

The best way is by using the Unit Circle...which is basically a circle with a radius of one on the x-y coordinate. If you already know the values of 30, 45, and 60 degrees, this will help.

Unit Circle: x² + y² = 1 (graph this out)

Now, the degrees start out at (1, 0) and rotate counterclockwise.

sin = y
cos = x
tan = y/x (x cannot equal 0)

So at: cos 0 degrees: you would get 1 (as 1,0) = 0.
at sin 90 degrees, you would get 1 (0, 1)

cos 30 = 1/2 (30 degrees is at (1/2, √3/2) on unit circle
cos 45 = √2/2 (45 degrees is at (√2/2, √2/2)
cos 60 = √3/2 (60 degrees is at (√3/2, 1/2) on unit circle
cos 90 = 0 (as 90 degrees is at (0, 1)

Now we're getting into the second quadrant
cos (90+30)
cos 120 = (-√3/2 (120 degrees is at (-√3/2, 1/2)

cos (90+45)
cos 135 = -√2/2 (135 degrees is at (-√2/2, √2/2)

As you can see, there is a systematic approach and it will help you memorize the values for the most commonly used angles.

As with above, you know that 135 degrees is in the 2nd quadrant (1st is 0-90, 2nd is 90-180, etc)...you know that 2nd quadrant is negative for x and positive for y.

Everything else is just relating it to the values for 30, 45, 60, which you already know.

Study the unit circle.

Good luck!

Answer 3

135° is in 2nd quadrant and therefore cos 135° is a - ve value.
cos 135° = - cos (180 - 45)°
cos 135° = - cos 45°
cos 135° = - 1 / √2 = - √2 / 2