University:
Felician University
Course:
MATH-231 | Geometry I
Academic year:

2023
Views:

58

Pages:

3
Author:

SpaceCadet101

Fill In The Blanks FUNCTION ALTERNATIVE NOTATION DOMAIN RANGE [y=sin^{-1}x] [y=cos^{-1}x] [y=tan^{-1}x] [y=arctan~x] Without restrictions, NO Trigonometric Function has an INVERSE function Evaluate Expression WITHOUT Using a Calculator [arcsin\frac{1}{2}=30^{\circ}] [arccos\frac{1}{2}=60^{\circ}] [cos^{-1}(-\frac{\sqrt{3}}{2})=150^{\circ}] [arctan(-1)=-45^{\circ}] [tan^{-1}(0)=0^{\circ}] [sin^{-1}(0)=0^{\circ}] [arccos~1=0^{\circ}] [arcsin~1=90^{\circ}] [arctan\sqrt{3}=60^{\circ}] [cos^{-1}(\frac{\sqrt{2}}{2})=45^{\circ}] [sin^{-1}(\frac{\sqrt{3}}{2})=60^{\circ}] Use a Calculator to Evaluate Expression. (Round your result to the nearest thousandth. If result does not exist, state why it does not exist.) sin⁻¹(2.1) does not exist arccos(0.341) ≈ 70.1° or 1.223 arcsin(-0.876) ≈ -61.2° or -1.068 cos⁻¹(0.197) ≈ 78.6° or 1.372 tan⁻¹(37.14) ≈ 88.8° or 1.549 Use the Properties of Inverse Trigonometric Functions to Evaluate the Expression. Simplify expression if necessary. sin(sin⁻¹(0.3)) = 0.3 cos(cos⁻¹(-0.1)) = -0.1 arcsin(sin(3π)) = π tan(arctan(4.5)) = 4.5 arcsin(sin(-0.2)) = -0.2 cos(cos⁻¹(π/2)) = 0 Find the Exact Value of the Expression WITHOUT Using a Calculator (HINT: sketch a right triangle) sin(arctan(3/4)) = 3/5 **Write an Algebraic Expression that is Equivalent to the Given Expression (HINT: sketch a right triangle)** 32. sin(arctan x) sinθ = x / √(x² + 1) right triangle with sides x and 1, hypotenuse √(x² + 1) 33. cos(sin⁻¹(2x)) cosθ = √(1 - 4x²) / 1 right triangle with sides x and √(9 x²), hypotenuse 3 34. tan(arccos(x/3)) tanθ = √(9 - x²) / x