Given cos(θ)=149 The gold angle stays fixed. Explore how a ray meets the tangent line x = 1.Show worked answer
Answer: 115196
sin2(θ)=1−(149)2=196115.
csc2(θ) is the reciprocal of sin2(θ).
Thus csc2(θ)=115196.
Example 2
Which values are excluded from the domain of sec(8x)? In each option, k is any integer.
For sec(8x), the probe represents the argument 8x. Explore where the line through the origin meets x = 1. Near vertical, the intersection can lie beyond this view.Show worked answer
Answer: x=16π+8kπ
sec(8x) has cos(8x) in its denominator.
Exclude 8x=2π+kπ. Dividing by 8 gives x=16π+8kπ.
Example 3
For an acute angle θ,cos(θ)=189. Find sec(θ).
Given cos(θ)=189 The gold angle stays fixed. Explore how a ray meets the tangent line x = 1.Show worked answer
Answer: 2
sec(θ)=cos(θ)1.
Therefore sec(θ)=2.
Further trigonometric functions practice | Year 11 Specialist | Ascent Arcade