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Finding Exact Values of Trig Functions
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How to find the exact value of any trig function:
Determine which quadrant the angle is in (sketch the angle if needed)
If it's a quadrantal angle (0, pi/2, pi...), you can easily evaluate it by just drawing a point and plugging in the for the definition of the trig function. (Ex: sin(pi/2) = 1, since at pi/2 x=0, y=1, and r=1)
If it's in the first quadrant, you can easily evaluate it by the table you have memorized.
If it's not in the first quadrant, then find the reference angle. Remember that you can add or subtract any multiple of 2pi to the angle and the value of the trig function at that angle will still be the same. Once you find the reference angle, you can evaluate the function at that angle and then determine if it is positive or negative based on which quadrant the original angle is in.
That's it! Hope this helps!
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Determine which quadrant the angle is in (sketch the angle if needed)
If it's a quadrantal angle (0, pi/2, pi...), you can easily evaluate it by just drawing a point and plugging in the for the definition of the trig function. (Ex: sin(pi/2) = 1, since at pi/2 x=0, y=1, and r=1)
If it's in the first quadrant, you can easily evaluate it by the table you have memorized.
If it's not in the first quadrant, then find the reference angle. Remember that you can add or subtract any multiple of 2pi to the angle and the value of the trig function at that angle will still be the same. Once you find the reference angle, you can evaluate the function at that angle and then determine if it is positive or negative based on which quadrant the original angle is in.
That's it! Hope this helps!
Facebook:
Instagram:
Thanks for watching! Comment below with any questions / feedback and make sure to like / subscribe if you enjoyed!
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