Find the exact value of the trigonometric function at the given real number. NS

glamrockqueen7

glamrockqueen7

Answered question

2021-10-29

Find the exact value of the trigonometric function at the given real number.
sin7π4

Answer & Explanation

liannemdh

liannemdh

Skilled2021-10-30Added 106 answers

We would like to find the exact value of sin7π4, First, we can find the reference angle of 7π4 where 2π7π4=π4, so the reference angle is π4.
Now the next step is to define the sign of sin7π4. We know that 7π4 is in quadrant 3 which the sine function is negative in this quadrant, so the value of sin7π4 is negative and we can simplify it as follows:
sin7π4=sin(2ππ4)=sinπ4
Note that the first step was to find the reference angle and then was to define the sign of sin7π4.
Now we can find the value of sin7π4 by knowing the value of sinπ4 which equals 22
sin7π4=sin(2ππ4)=sinπ4=22

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