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A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
A day full of math games & activities. Find one near you.
tan (θ + φ); cos(θ) = −1/3, θ in Quadrant III, sin(φ) = 1/4, φ in Quadrant II. Evaluate the expression.
Solution:
Given:
cos(θ) = −1/3, θ in Quadrant III
sin(φ) = 1/4, φ in Quadrant II
To find: tan (θ + φ)
To evaluate the trigonometric expression, let us determine θ and Φ using inverse trigonometric functions.
Θ = 180° + cos⁻¹(1/3)
= 180° + 70.5°
= 250.5°
Φ = 180° - sin⁻¹(1/4)
= 180°- 14.4°
= 165.5°
tan (θ + φ) = tan( 250.5° + 165.5°)
= tan(416°)
= tan(360° +56°)
= tan(56°)
= 1.48
tan (θ + φ); cos(θ) = −1/3, θ in Quadrant III, sin(φ) = 1/4, φ in Quadrant II evaluate the expression.
Summary:
If cos(θ) = −1/3, θ in Quadrant III, sin(φ) = 1/4, φ in Quadrant II, then the value of tan (θ + φ) is 1.48.
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