Worksheet: Evaluating Trigonometric Functions

In this worksheet, we will practice finding the value of a trigonometric function from a given value of another trigonometric function.


Find csc𝜃 given tan𝜃=247 and cos𝜃<0.

  • A2524
  • B257
  • C2524
  • D257


Find the value of cos(180𝜃) given sin𝜃=35 where 270<𝜃<360.

  • A45
  • B45
  • C34
  • D34


Find all the trigonometric ratios of 𝜃 given cot𝜃=815 where 𝜃3𝜋2,2𝜋.

  • Asin𝜃=1517, cos𝜃=817, tan𝜃=158, csc𝜃=1715, sec𝜃=178
  • Bsin𝜃=1517, cos𝜃=817, tan𝜃=158, csc𝜃=1715, sec𝜃=178
  • Csin𝜃=1517, cos𝜃=817, tan𝜃=158, csc𝜃=1715, sec𝜃=178
  • Dsin𝜃=1517, cos𝜃=817, tan𝜃=158, csc𝜃=1715, sec𝜃=178


Given that cot(𝜃)=32, where 𝜋2<𝜃<𝜋, evaluate sec(𝜃) without using a calculator.

  • A139
  • B913
  • C913
  • D139
  • E52


Given that csc𝜃=76 and tan𝜃>0, find cos𝜃.

  • A137
  • B67
  • C136
  • D67
  • E137


Given that sin(𝜃)=13, where 𝜋<𝜃<3𝜋2, evaluate csc(2𝜃) without using a calculator.

Hint: Take cscsincos(2𝜃)=12(𝜃)(𝜃).

  • A924
  • B928
  • C928
  • D229
  • E429


Given that sin(𝜃)=13, where 0<𝜃<𝜋2, and cos(𝜃)=14, where 0<𝜃<𝜋2, evaluate cos(𝜃+𝜃) without using a calculator.

Hint: Take coscoscossinsin(𝜃+𝜃)=(𝜃)(𝜃)(𝜃)(𝜃).

  • A15+2212
  • B152212
  • C26
  • D152212
  • E15+2212


Given that cos(𝜃)=13, where 0<𝜃<𝜋2 and cos(𝜃)=13, where 0<𝜃<𝜋2, evaluate tan(𝜃+𝜃) without using a calculator.

Hint: Take tantantantantan(𝜃+𝜃)=(𝜃)+(𝜃)1(𝜃)(𝜃).

  • A924
  • B728
  • C728
  • D427
  • E427

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