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In this lesson, we will learn how to solve trigonometric equations using cofunction identities.

Q1:

Find the value of s e c ( 9 0 + π ) β given c s c π = 1 7 8 where 0 < π < 9 0 β β .

Q2:

Find all the possible general solutions for the equation s i n c o s π = 5 π .

Q3:

Find the value of c s c s e c c s c ( 5 6 ) ( 3 4 ) + ( 1 8 0 β π ) β β β given t a n c o t ( π + 1 0 ) ( π + 2 0 ) = 1 β β .

Q4:

Find the general solution of the equation s i n ( 9 0 β π ) = 1 2 β .

Q5:

Find s i n 6 π given c o s s i n 2 π = 7 π where π is a positive acute angle.

Q6:

Find the value of c o t ( π β 9 0 ) β given s e c π = β 1 7 1 5 where 9 0 < π < 1 8 0 β β .

Q7:

Find the measure of β π given c s c s e c ( π + 1 5 2 4 β² ) = ( π + 3 7 5 4 β² ) β β where π is a positive acute angle. Give the answer to the nearest minute.

Q8:

Find the value of c o s ( 1 8 0 + π ) β given s i n ( 9 0 β π ) = β 7 1 7 β where π is the smallest positive angle.

Q9:

Find s i n 8 π given s e c ( 9 0 + π ) β 2 = 0 β where 1 8 0 < π < 2 7 0 β β .

Q10:

Find the value of c o t ο» π 2 β 2 π΅ ο given t a n π΅ = β 3 2 where 3 π 2 < π΅ < 2 π .

Q11:

Find all possible solutions of π that satisfy c o s s i n 2 π β 6 π = 0 .

Q12:

Find the value of β π given c o s s i n οΌ 3 2 π ο β π = 0 where π is a positive acute angle.

Q13:

Find the value of π that satisfies s i n c o s ο» 4 π β π 3 ο = 4 π where π β ο 0 , π 2 ο .

Q14:

Find s i n c o s 3 π + 6 π given c o t t a n π = 2 π where π is a positive acute angle.

Q15:

Find π β π΅ given π β π΄ = 4 3 β and s i n c o s π΅ = π΄ where π΅ is an acute angle. Give the answer to the nearest degree.

Q16:

Find the value of c s c c o t t a n c s c ( 9 0 + πΌ ) ( 2 7 0 + π½ ) ( 2 7 0 β πΌ ) ( 2 7 0 + π½ ) β β β β given 1 7 πΌ β 8 = 0 s i n , where 0 < π < 9 0 β β , and 3 π½ + 4 = 0 t a n where π½ is the largest angle in the range ] 0 , 3 6 0 [ β β .

Q17:

Find π in degrees given c s c s e c ( π β 5 ) = ( 6 π β 1 0 ) β β where π is a positive acute angle.

Q18:

Find π in degrees given c o s s i n ( π + 2 5 ) = ( 3 π + 5 ) β β where π is a positive acute angle.

Q19:

Find the value of s i n ( 9 0 β π ) β given s i n π = β 3 5 where 1 8 0 β€ π < 2 7 0 β β .

Q20:

Find the value of π given c o s s i n ( π + 6 ) = 5 1 β β where ( π + 6 ) β is an acute angle.

Q21:

Find the value of s i n ( 2 7 0 β π ) β given s i n π = 1 2 1 3 where 9 0 < π < 1 8 0 β β .

Q22:

Find the value of c o t ( 2 7 0 + π ) β given t a n π = β 4 3 where 9 0 < π < 1 8 0 β β .

Q23:

Find c o t ( 9 0 β 3 π ) β given t a n c o t π = 5 π where π is a positive acute angle.

Q24:

Find the value of s i n t a n t a n ( 1 8 0 β π ) + ( 9 0 β π ) β ( 2 7 0 β π ) β β β given c o s π = β 4 5 where 9 0 < π < 1 8 0 β β .

Q25:

Find the value of c o s c o s ( 3 6 0 β π΅ ) β ( 9 0 β π΅ ) β β given t a n π΅ = 4 3 where 0 < π΅ < π 2 .

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