Worksheet: Evaluating Trigonometric Functions Using Cofunction Identities

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

Q1:

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

  • A817
  • B1517
  • 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(270𝜃) given cos𝜃=45 where 90<𝜃<180.

  • A43
  • B43
  • C34
  • D34

Q4:

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

  • A45
  • B45
  • C35
  • D35

Q5:

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

  • A234
  • B13920
  • C13920
  • D234

Q6:

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

  • A14
  • B34
  • C14
  • D34

Q7:

Find the value of sinsincos(90𝑥)(𝑥)(902𝑥).

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

Q8:

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

  • A34
  • B34
  • C54
  • D54

Q9:

Simplify sincos𝜃(𝜃).

Q10:

Find the value of tan5𝜋6.

  • A22
  • B33
  • C33
  • D22
  • E12

Q11:

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

  • A54
  • B54
  • C53
  • D53

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(𝜃270).

  • Asin𝜃
  • B𝜃cos
  • Ccos𝜃
  • D𝜃sin

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(2𝜋𝜃).

Q18:

Given that sin𝜃=38, find the value of sin(2𝜋𝜃).

  • A38
  • B58
  • C58
  • D38
  • E83

Q19:

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

  • A1312
  • B125
  • C512
  • D135

Q20:

Find sec(90𝜃) 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 27,357.

  • A3553
  • B72
  • C72
  • D27

Q22:

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

  • A2
  • B32
  • C12
  • D12

Q23:

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

  • A32
  • B155
  • C23
  • D32

Q24:

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

  • A33
  • B2
  • C33
  • D3

Q25:

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

  • A32
  • B23
  • C23
  • D53

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