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In this lesson, we will learn how to solve simple trigonometric equations.

Q1:

What is the general solution of s i n π = β 2 2 ?

Q2:

Find the value of π given t a n οΌ π 4 ο = β 3 where π 4 is an acute angle.

Q3:

Find the solution set of t a n t a n t a n t a n π₯ + 7 + π₯ 7 = 1 β β , where 0 < π₯ < 3 6 0 β β .

Q4:

Find the solution set of s i n c o s c o s s i n π₯ 1 6 β π₯ 1 6 = β 2 2 β β , where 0 < π₯ < 3 6 0 β β .

Q5:

Find the solution set of π₯ given t a n t a n t a n t a n π₯ β 6 4 1 + π₯ 6 4 = 1 β β where 0 < π₯ < 3 6 0 β β .

Q6:

Suppose π is a point on a unit circle corresponding to the angle of 4 π 3 . Is there another point on the unit circle representing an angle in the interval [ 0 , 2 π [ that has the same tangent value? If yes, give the angle.

Q7:

Consider , a point on a unit circle corresponding to the angle of . Is there another point on the unit circle that has the same -coordinate as and represents an angle in the interval ? If yes, give the angle.

Q8:

Find the set of values satisfying 4 π β 1 = 0 s i n 2 where 9 0 β€ π β€ 3 6 0 β β .

Q9:

Find the general solution to the equation c o t ο» π 2 β π ο = β 1 β 3 .

Q10:

Suppose is a point on a unit circle corresponding to the angle of . Is there another point on the unit circle that represents an angle in the interval and has the same -coordinate as ? If yes, give the angle.

Q11:

Find the set of values satisfying c o s ( π β 1 0 5 ) = β 1 2 where 0 < π < 3 6 0 β β .

Q12:

Find π in degrees given c o s ( 9 0 + π ) = β 1 2 β where π is the smallest positive angle.

Q13:

Find the set of values satisfying β 2 π π β π = 0 s i n c o s c o s where 0 β€ π < 3 6 0 β β .

Q14:

Find the solution set for π₯ given c o s c o s s i n s i n π₯ 2 π₯ β π₯ 2 π₯ = 1 2 where 0 < π₯ < 3 6 0 β β .

Q15:

Find the solution set for π₯ given s i n c o s c o s s i n π₯ 3 5 + π₯ 3 5 = β 2 2 β β where 0 < π₯ < 3 6 0 β β .

Q16:

Find the solution set of π given t a n t a n t a n t a n 2 5 π β 2 3 π 1 + 2 5 π 2 3 π = β 3 where 0 < π < 9 0 β β .

Q17:

Find the solution set of the equation s i n s i n s i n s i n ( 6 7 + 2 π ) ( 7 9 + π ) + ( 2 3 β 2 π ) ( 1 1 β π ) = 1 β β β β given 0 < π < π 2 .

Q18:

Find the set of possible values of π₯ which satisfy 1 β π₯ β π₯ = 2 c o s c o s 2 4 where 0 < π₯ < 3 6 0 β β .

Q19:

Find π β π given c o s s i n s i n c o s 3 4 . 5 3 4 . 5 + 1 2 6 9 = π β β β where π is a positive acute angle.

Q20:

Find the set of solutions in the range 0 < π₯ < 1 8 0 for the equation ( π₯ + π₯ ) = 2 2 π₯ s i n c o s s i n 2 2 .

Q21:

Find the solution set of given , where .

Q22:

What is the general solution of c o s π = β 3 2 ?

Q23:

Find the set of values satisfying 1 1 π + 1 3 = 0 t a n where 0 β€ π < 3 6 0 β β . Give the answers to the nearest second.

Q24:

Find all the possible general solutions of c o s s i n c o s π π = β 2 2 π .

Q25:

Find the set of values satisfying c o s 2 π₯ = β β 3 2 , where 0 β€ π₯ < 2 π .

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