Worksheet: Evaluating Trigonometric Functions Using Cofunction Identities

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In this worksheet, we will practice using cofunction and odd/even identities to find the values of trigonometric functions.

Q1:

Find sin𝜃 given 51(90−𝜃)=24cos∘ where 𝜃 is a positive acute angle.

  • A−817
  • B−1517
  • C1517
  • D817

Q2:

Which of the following is equal to sin𝜃?

  • Acos𝜋2+𝜃
  • Bcos3𝜋2+𝜃
  • Csin3𝜋2+𝜃
  • Dsin𝜋2+𝜃

Q3:

Find the value of tan(270−𝜃)∘ given cos𝜃=−45 where 90<𝜃<180∘∘.

  • A43
  • B−43
  • C−34
  • D34

Q4:

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

  • A−45
  • B45
  • C35
  • D−35

Q5:

Find the value of sintansin(180−𝑥)+(360−𝑥)+7(270−𝑥)∘∘∘ given sin𝑥=35 where 0<𝜃<90∘∘ .

  • A234
  • B13920
  • C−13920
  • D−234

Q6:

Find the value of sincostancot(−60)30+5733∘∘∘∘ giving the answer in its simplest form.

  • A−14
  • B34
  • C14
  • D−34

Q7:

Find the value of sinsincos(90−𝑥)(𝑥)(90−2𝑥).

  • A1
  • Bcos(90−𝑥)
  • C12
  • D2
  • Esin(2𝑥)

Q8:

𝐴𝐵𝐶 is a right-angled triangle at 𝐵. Find cot𝛼 given cot𝜃=43.

  • A34
  • B−34
  • C−54
  • D54

Q9:

Simplify sincos−𝜃(−𝜃).

Q10:

Find the value of tan−5𝜋6.

  • A√22
  • B√33
  • C−√33
  • D−√22
  • E12

Q11:

Find the value of csc(−𝜃) given sin𝜃=−45 where 180<𝜃<270∘∘.

  • A54
  • B−54
  • C53
  • D−53

Q12:

In the figure, points 𝑀(𝜃,𝜃)cossin and 𝑁 lie on the unit circle, and ∠𝐴𝑂𝑁=𝜋+𝜃.

Express the values of sine, cosine, and tangent of 𝜋+𝜃 in terms of their values for 𝜃. Check whether this is valid for all values of 𝜃.

  • Acoscossinsintantan(𝜋+𝜃)=𝜃,(𝜋+𝜃)=−𝜃,(𝜋+𝜃)=𝜃
  • Bcoscossinsintantan(𝜋+𝜃)=−𝜃,(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃
  • Ccoscossinsintantan(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃,(𝜋+𝜃)=𝜃
  • Dcoscossinsintantan(𝜋+𝜃)=−𝜃,(𝜋+𝜃)=−𝜃,(𝜋+𝜃)=𝜃
  • Ecoscossinsintantan(𝜋+𝜃)=−𝜃,(𝜋+𝜃)=−𝜃,(𝜋+𝜃)=−𝜃

Q13:

Simplify sin(𝜃−270)∘.

  • Asin𝜃
  • B−𝜃cos
  • Ccos𝜃
  • D−𝜃sin

Q14:

Find the value of seccsc10515∘∘.

Q15:

Find 𝜃 in degrees given cossin15315′=−𝜃∘ where 𝜃 is an acute angle.

  • A11645′∘
  • B6315′∘
  • C20645′∘
  • D2645′∘

Q16:

Find 𝜃 in degrees given csccsc32745′=−𝜃∘ where 𝜃 is an acute angle.

  • A2215′∘
  • B5745′∘
  • C4745′∘
  • D3215′∘

Q17:

Given that tan𝜃=−18, find the value of tan(2𝜋−𝜃).

Q18:

Given that sin𝜃=−38, find the value of sin(2𝜋−𝜃).

  • A38
  • B−58
  • C58
  • D−38
  • E83

Q19:

Find tan(90−𝜃)∘ given 𝜃 is in standard position and its terminal side passes through the point 513,1213.

  • A1312
  • B125
  • C512
  • D135

Q20:

Find sec(90−𝜃)∘ given 𝜃 is in standard position and its terminal side passes through the point 35,45.

  • A45
  • B54
  • C53
  • D43

Q21:

Find csc(90+𝜃)∘ given 𝜃 is in standard position and its terminal side passes through the point 27,3√57.

  • A35√53
  • B72
  • C−72
  • D27

Q22:

Find sin(90+𝜃)∘ given 𝜃 is in standard position and its terminal side passes through the point 12,√32.

  • A−2
  • B−√32
  • C−12
  • D12

Q23:

Find csc(270−𝜃)∘ given 𝜃 is in standard position and its terminal side passes through the point 23,√53.

  • A32
  • B15√5
  • C23
  • D−32

Q24:

Find tan(270−𝜃)∘ given 𝜃 is in standard position and its terminal side passes through the point 12,√32.

  • A−√33
  • B−2
  • C√33
  • D√3

Q25:

Find sin(270+𝜃)∘ given 𝜃 is in standard position and its terminal side passes through the point 23,√53.

  • A−32
  • B−23
  • C23
  • D−√53

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