Lesson: Trigonometric Identities and Double Angles

In this lesson, we will learn how to use the Pythagorean identity and double-angle formulas to derive further trigonometric identities and evaluate trigonometric expressions.

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Worksheet: Trigonometric Identities and Double Angles • 20 Questions

Q1:

Find the value of t a n c o t 2 2 𝜃 + 𝜃 given t a n c o t 𝜃 + 𝜃 = 1 7 .

Q2:

Find the value of s i n c o s 𝜃 𝜃 given s i n c o s s i n c o s 2 2 𝜃 𝜃 𝜃 𝜃 = 5 3 .

Q3:

For any 𝑥 0 + 𝑘 𝜋 ( 𝑘 ) , what is s i n 2 𝑥 ?

Q4:

For any 𝑥 𝜋 2 + 𝑘 𝜋 ( 𝑘 ) , what is 1 + 𝑥 t a n 2 ?

Q5:

Simplify ( 𝑎 1 ) 1 𝑎 t a n t a n .

Q6:

Find the value of t a n 2 𝑋 given t a n t a n 𝑋 1 𝑋 = 2 2 .

Q7:

Find the value of s e c c s c 𝑋 + 𝑋 given s i n c o s 𝑋 + 𝑋 = 6 7 where 𝜋 2 < 𝑋 < 𝜋 .

Q8:

Find, without using a calculator, the value of s i n c o s 2 𝐵 2 2 𝐵 given c o s 𝐵 = 4 5 where 3 𝜋 2 < 𝐵 < 2 𝜋 .

Q9:

For any 𝑥 𝑘 𝜋 ( 𝑘 ) , what is 1 + 𝑥 c o t 2 ?

Q10:

Knowing that c o s 𝑥 = 1 7 5 and that 3 𝜋 2 𝑥 2 𝜋 , find s i n 𝑥 .

Q11:

For any 𝑥 𝜋 2 + 𝑘 𝜋 ( 𝑘 ) , what is c o s 2 𝑥 ?

Q12:

Find the value of t a n 𝜃 given s e c t a n 𝜃 𝜃 = 2 1 3 where 0 < 𝜃 < 𝜋 2 .

Q13:

Find the value of 7 𝜃 𝜃 t a n s e c 2 2 2 .

Q14:

Knowing that c o s 𝑥 = 3 5 and that 𝜋 𝑥 3 𝜋 2 , find t a n 𝑥 .

Q15:

Knowing that t a n 𝑥 = 2 1 9 and 0 𝑥 𝜋 2 , find s i n 𝑥 .

Q16:

Find the value of c s c 2 𝜃 given c o t 𝜃 = 7 9 .

Q17:

Knowing that s i n 𝑥 = 7 4 and 3 𝜋 2 𝑥 2 𝜋 , find c o s 𝑥 .

Q18:

Find the value of c o s c o s s i n s i n 𝛼 𝛽 + 𝛼 𝛽 , given s i n 𝛼 = 8 1 7 where 𝛼 𝜋 2 , 𝜋 and 1 7 𝛽 8 = 0 c o s where 𝛽 3 𝜋 2 , 2 𝜋 .

Q19:

Find the value of c o t c s c t a n s e c 𝜃 𝜃 𝜃 𝜃 given 𝜃 3 𝜋 2 , 2 𝜋 and s i n 𝜃 = 4 5 .

Q20:

Find 8 1 𝜃 𝜃 s i n c o s given s i n c o s 𝜃 𝜃 = 1 9 where 𝜃 0 , 𝜋 2 .

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