use the appropriate trig identity (sum and difference, half angle, double angle) to find the exact value. 1)cos 255 degrees
2) sin 165 degrees
3) tan 285 degrees
isn't 255 = 180+75=270-15 which is 270-30/2?
isn't 165=180-30/2
isn't 285=270+30/2?
To find the exact values of the trigonometric functions using the appropriate trig identities, follow these steps:
1) cos 255 degrees:
- First, determine if this angle can be written as the sum or difference of angles that have known trigonometric values.
- To express 255 degrees as a sum or difference of angles, we can use the fact that cos (180 degrees + x) = -cos x.
- Since 255 degrees is greater than 180 degrees, we rewrite it as 255 degrees = 180 degrees + 75 degrees.
- Now, we can use the identity cos (180 degrees + x) = -cos x to solve for cos 255 degrees:
cos 255 degrees = cos (180 degrees + 75 degrees) = -cos 75 degrees
2) sin 165 degrees:
- Similar to the previous question, determine if this angle can be expressed as the sum or difference of angles that have known trigonometric values.
- To express 165 degrees as a sum or difference of angles, we can use the fact that sin (180 degrees - x) = sin x.
- Since 165 degrees is less than 180 degrees, we rewrite it as 180 degrees - 15 degrees.
- Now, we can use the identity sin (180 degrees - x) = sin x to solve for sin 165 degrees:
sin 165 degrees = sin (180 degrees - 15 degrees) = sin 15 degrees
3) tan 285 degrees:
- For this question, we can use the identity tan (x + 180 degrees) = tan x to find the equivalent angle.
- Since 285 degrees can be expressed as 105 degrees + 180 degrees, we can use the identity to solve for tan 285 degrees:
tan 285 degrees = tan (105 degrees + 180 degrees) = tan 105 degrees
To find the exact values for each trigonometric function in the respective questions, consult a trigonometric table or use a calculator with a trigonometric function feature.