Find sin(7pie/4) using exact values

Use a reference angle. 7Pi/4 lies in the 4th quadrant, exactly Pi/4 radians less than 2Pi, therefore the reference angle is Pi/4. Since sine values are negative in the 4th quadrant, you'll need to use the exact value for sine of Pi/4, but the answer will be negative due to the quadrant the angle falls within.

Okay so how would you do that for sec(2pie/3)?

Same game plan. Any time an angle is more than Pi/2 (ie, past 1st quadrant), then you look for the reference angle - that's the smallest angle that will take you back to the x-axis, and is found by either adding to or subtracting from Pi or 2Pi. In this case, 2Pi/3 (which is 120 degrees) sits in Quadrant 2, and is Pi/3 away from Pi. (IE, Pi-2Pi/3 = Pi/3). So, first think of what the cosine of Pi/3 would be as an exact value. Then take the reciprocal of that (since secant is the reciprocal of cosine). Lastly, the answer will have to be negative since cosine & secant are negative in Quadrant 2. (IE, the old ASTC rule).

OKAY I remember now, thank you so much.

No problem!

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