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Using reference angles to evaluate trigonometric functions?
sin135
(@)=180-135=45 degrees
What i don't get is that the function value or the reference angle is sin45 which equals √ 2/2. I don't understand how do you find the function value when no actual point is given. The only thing i know is that sin=y/r... but whats r? no points so i can't do it from my understanding.
the example gives the answer like this:
180-135=45 degree
the function value for the reference angle is sin45=√ 2/2.
angle 135 of sin lies in quadrant II therefore we put a + sign before the function value of the reference angle:
in135=+sin45=√ 2/2
2 Answers
- TomVLv 71 decade agoFavorite Answer
The reference angle is the acute angle between the angle's terminal line and the x-axis. Since its an acute angle, it will always be less than 90°.
To convert a given angle that is greater than 90° to its reference angle:
1. If the angle is less than 180°, subtract the angle from 180°
2. If the angle is greater than 180°, subtract 180 from the angle.
Repeat either 1 or 2 as appropriate until the result is between 0 and 90°.
The absolute values of the trigonometric functions of the original angle are equal to those of the reference angle. The signs of the trigonometric functions of the original angle are chosen based on the Quadrant that contains the terminal lie of the original angle.
Q1: all functions are positive
Q2: sine and cosecant positive; cosine, secant, tangent, cotangent negative.
Q3: tangent and cotangent positive; sine, cosecant, cosine, secant negative,
Q4: cosine, secant postitive; sine, cosecant, tangent, cotangent negative.
