Worksheet: Evaluating Trigonometric Functions Using Pythagorean Identities

In this worksheet, we will practice using the Pythagorean identities to find the values of trigonometric functions.

Q1:

Find cos𝜃 given sin𝜃=35 where 270𝜃<360.

  • A34
  • B35
  • C45
  • D45

Q2:

Find cot𝜃 given sin𝜃=35 where 90<𝜃<180.

  • A43
  • B34
  • C43
  • D34

Q3:

Find the value of cot𝜃 given csc𝜃=259.

  • A43
  • B169
  • C1625
  • D916

Q4:

Find the value of sin𝜃 given cos𝜃=2129 where 90<𝜃<180.

  • A2029
  • B2029
  • C2021
  • D2021
  • E2129

Q5:

Find the value of sincos𝜃𝜃 given sincos𝜃+𝜃=54.

  • A932
  • B916
  • C132
  • D18

Q6:

Find the value of 2𝜃𝜃sincos given 12𝜃+5=0tan where 180<𝜃<360.

  • A524
  • B524
  • C120169
  • D120169

Q7:

Find sectan𝜃𝜃 given sectan𝜃+𝜃=1427.

  • A2714
  • B4114
  • C4114
  • D2714

Q8:

Find the value of sec𝜃 given sectan𝜃𝜃=16 where 0<𝜃<𝜋2.

  • A3718
  • B3712
  • C3512
  • D209

Q9:

Knowing that sin𝑥=137 and 𝜋2𝑥𝜋, find tan𝑥.

  • A1336
  • B613
  • C136
  • D613
  • E136

Q10:

Find the value of tan(360𝜃) given cot𝜃=43 where 0<𝜃<90.

  • A43
  • B34
  • C34
  • D43

Q11:

Find the value of tan(180+𝜃) given sin𝜃=35 where 0<𝜃<90.

  • A45
  • B34
  • C45
  • D34

Q12:

Find cscsec𝑎𝑎 given cossin𝑎𝑎=27.

  • A2845
  • B4514
  • C2845
  • D1445

Q13:

Simplify sinsin𝜃+(90𝜃).

Q14:

Find sin𝐴, given 𝐴𝐵𝐶 is a right triangle at 𝐵 where cos𝐴=0.8.

  • A45
  • B43
  • C35
  • D53
  • E54

Q15:

Find 1+𝐴tan, given 𝐴𝐵𝐶 is a right-angled triangle at 𝐶 where 𝐴𝐵=10cm and 𝐵𝐶=6cm.

  • A732
  • B1116
  • C3532
  • D2516

Q16:

Find the value of cscsintancsc𝜃𝜃𝜃𝜃 given 𝜃𝜋2,𝜋 and cos𝜃=45.

  • A94
  • B14
  • C94
  • D14

Q17:

Find the value of cscsintancotcos𝜃𝜃𝜃𝜃+𝜃 given 𝜃𝜋,3𝜋2 and sin𝜃=45.

  • A925
  • B5925
  • C5925
  • D925

Q18:

Find the value of sec(𝜃) given csc𝜃=135 where 0<𝜃<90.

  • A1312
  • B1213
  • C1312
  • D1213

Q19:

Find the value of 17𝜃+9𝜃+8𝜃sincossec.

Q20:

Find the value of sincoscossin𝛼𝛽𝛼𝛽, given tan𝛼=34 where 𝛼 is the smallest positive angle and tan𝛽=158 where 180<𝛽<270.

  • A1385
  • B1385
  • C3685
  • D3685

Q21:

Find tan𝜃 given sin𝜃=35 where 270𝜃<360.

  • A43
  • B34
  • C34
  • D43

Q22:

Find the value of sec(1,080+𝜃) given 4𝜃3=0tan where 0<𝜃<180.

  • A54
  • B53
  • C53
  • D54

Q23:

Find the value of 35𝛼16𝛼sincot given cos𝛼=925 where 180<𝛼<270.

Q24:

Find the value of tan𝜃 given csc𝜃=53 where 180<𝜃<270.

  • A34
  • B45
  • C34
  • D35
  • E45

Q25:

Find the value of sincos(180+𝛼)+(180𝛽) given 5𝛼3=0sin where 0<𝛼<90 and 4𝛽+3=0tan where 𝛽 is the largest angle in the range 0<𝛽<360.

  • A75
  • B15
  • C15
  • D75

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