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Right Triangle Trigonometry Practice

Practice 1

The sec θ = 3. Find the other five trigonometric functions.

secant theta equals h of y p over a. d j equals three oneths

Using this information, fill in the side lengths.


Answer:

Now use the Pythagorean theorem to find the missing side length.

  • ____(Fill in the blank)2 = ____(Fill in the blank)2 + b2
  • ____(Fill in the blank) − ____(Fill in the blank) = b2
  • ____(Fill in the blank) = b2



  • Answer:
  • 32 = 12 + b2
  • 9 − 1 = b2
  • 8 = b2


Practice 1

The sec θ = 3. Find the other five trigonometric functions.

secant theta equals h of y p over a. d j equals three oneths
  • sin θ = the fraction with numerator the square root of blank square and denominator the square root of blank

  • cosine theta equals the fraction with numerator blank and denominator blank

  • tangent theta equals blank the square root of blank

  • cosecant theta equals the fraction with numerator the square root of blank and denominator blank

  • sec θ = 3

  • cotangent theta equals the fraction with numerator the square root of blank and denominator blank
  • Answer:
  • sine theta equals 2 the square root of 2 over 3

  • cosine theta equals 1 third

  • tangent theta equals 2 the square root of 2

  • cosecant theta equals 3 the square root of 2 over 4

  • sec θ = 3

  • cotangent theta equals the square root of two over 4

  • cosecant theta equals 3 over 2 the square root of 2 the fraction with numerator the square root of 2 and denominator the square root of 2 equals 3 the square root of 2 over 4

  • cotangent theta equals 1 over 2 the square root of 2 the fraction with numerator the square root of 2 and denominator the square root of 2 equals the fraction with numerator the square root of 2 and denominator 4

Practice 2

Using the special angle table, confunctions relationships, and the trig identities for reciprocal and quotient identities, find the following given the angle θ = pi over 3

  • Find tan θ
  • pi over 3 corresponds to the point open paren one half comma the fraction with numerator the square root of 3 and denominator 2 close paren
  • tan θ is the y-value divided by the x-value of the point

    • tan pi over 3 = square root

  • Answer: tan pi over 3 = the square root of 3

  • the tangent of pi over 3 equals the fraction with numerator the square root of 3 slash 2 and denominator 1 slash 2 equals the square root of 3

  • Find cot open paren pi over 2 minus theta close paren

  • Using the cofunction relationships, which trig function is equal to cot open paren pi over 2 minus theta close paren?

  • cot open paren pi over 2 minus theta close paren = ____(Fill in the blank) θ square root

  • Answer: cot open paren pi over 2 minus theta close paren = tan θ = the square root of 3
  • the cotangent of open paren pi over 2 minus theta close paren equals tangent theta

Practice 3

Simplify the following expression.
tan x csc x cos x

Use the quotient identity for tan

  • blank x over blank x = csc x cos x

  • Answer: sine x over cosine x = csc x cos x

  • Use the reciprocal identity for csc
  • sine x over cosine x equals 1 over white medium square x cosine x

  • Answer: sine x over cosine x the fraction with numerator 1 and denominator the fraction with numerator sine and denominator x cosine x

  • Divide out the common factors
  • tan x csc x cos x = ____(Fill in the blank)

  • Answer:
  • Use the reciprocal identity for csc

  • tan x csc x cos x = 1