Question 38147: I need help using special right triangles to find the exact values of sines and cosines for each angle. For example: find the values of sine and cosine for the angle -135 degrees.
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! I need help using special right triangles to find the exact values of sines and cosines for each angle. For example: find the values of sine and cosine for the angle -135 degrees.
FIRST LEARN THE TRIGNOMETRIC RATIOS FOR STANDARD TRIANGLES.
THEN LEARN WHICH QUADRANT THE ANGLE IS
USE ALL SILVER TEA CUPS CONVENTION ,TO KNOW THE SIGN OF THE TRIGNOMETRIC RATIO.
IF ANGLE IS IN I QUADRANT ...THEN...ALL ARE +VE
...............II.......................SINE ONLY IS +VE
...............III......................TANGENT ONLY IS +VE
................IV.......................COSINE ONLY IS +VE.
NOW WRITE GIVEN ANGLE AS 0+X..OR...0-X...OR....180+ OR - X ....OR....360+ OR -X ETC....
YOUR EXAMPLE OF -135
SINE (0-135)=-SIN(135)..........0-X..MEANS IV Q...SINE IS -VE.
-1*SIN(135)=-SIN(180-45)=-SIN(45).....180-X MEANS II Q. SINE IS POSITIVE.
-1*SIN45=-1/SQRT(2)
GET BY HEART THE STANDARD TABLES FOR 0,30,45,60,90.
SIMILARLY COS (0-135)=COS(135)=COS(180-45)=-COS(45)=-1/SQRT2
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