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2 years ago

Part A: Given sine of theta is equal to radical 3 over 2 comma determine three possible angles θ on the domain [0,∞).

Mathematics

1 answer:

aliya0001 [1]2 years ago

4 0

Answer:

A. {60°, 120°, 420°}

B. θ = 15π/4; sec(θ) = √2

Step-by-step explanation:

The sine function is periodic with period 360°, and it is symmetrical about the line θ = 90°. The reference angle for the given value of sin(θ) is ...

θ = arcsin(√3/2) = 60°

The next larger angle with the same sine is (2×90°) -60° = 120°. Any multiple of 360° added to either one of these angles will give an angle with the same sine. A possible set of 3 angles is ...

{60°, 120°, 420°}

One degree is π/180 radians, so the given angle in radians is ...

θ = 675° = 675(π/180) radians = 15π/4 radians

This angle has the same trig function values as 7π4, a 4th-quadrant angle with a reference angle of π/4, or 45° The secant of that angle is

sec(45°) = √2

The 4th-quadrant angle has the same sign, so ...

sec(675°) = sec(15π/4) = √2

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