There are particularly six inverse trig functions for each trigonometry ratio. The inverse of six important trigonometric functions are: Arcsine Arccosine Arctangent Arccotangent Arcsecant Arccosecant Let us discuss all the six important types of inverse trigonometric functions along with its definition, formulas, graphs, properties and solved examples. Arcsine Function Arcsine function is an inverse of the… Continue reading Inverse Trigonometric Functions Graphs
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Formulas
The basic inverse trigonometric formulas are as follows: Inverse Trig Functions Formulas Arcsine sin-1(-x) = -sin-1(x), x ∈ [-1, 1] Arccosine cos-1(-x) = π -cos-1(x), x ∈ [-1, 1] Arctangent tan-1(-x) = -tan-1(x), x ∈ R Arccotangent cot-1(-x) = π – cot-1(x), x ∈ R Arcsecant sec-1(-x) = π -sec-1(x), |x| ≥ 1 Arccosecant cosec-1(-x)… Continue reading Formulas
Introduction
Inverse trigonometric functions are simply defined as the inverse functions of the basic trigonometric functions which are sine, cosine, tangent, cotangent, secant, and cosecant functions. They are also termed as arcus functions, antitrigonometric functions or cyclometric functions. These inverse functions in trigonometry are used to get the angle with any of the trigonometry ratios. The inverse trigonometry functions… Continue reading Introduction
Inverse Trigonometric Functions
We can use inverse trigonometric functions to find an angle with a given trigonometric value. We can also inverse trigonometric functions to solve a right triangle. Examples: Use the calculator to find an angle θ in the interval [0, 90] that satisfies the equation.a) sin θ = 0.7523b) tan θ = 3.54 Solve the given… Continue reading Inverse Trigonometric Functions
Determining Trig. Function value On Calculator
Using the TI 84 to find function values for sine, cosine, tangent, cosecant, secant, and cotangent. Examples: sin 30° cos 45° tan(-264°) sec(102.5°) csc(432°) cot(-23.45°)
Examples:
Use a calculator to find the function value. Use the correct number of significant digits.a) cos 369.18°b) tan 426,62°c) sin 46.6°d) cot 17.9° Determine θ in degrees. Use the correct number of significant digits.a) sin θ = 0.42b) cos θ = 0.29c) tan θ = 0.91 Determine θ in decimal degrees, 0° ≤ θ ≤… Continue reading Examples:
How To Use A Calculator To Find Trig Ratios And Angles?
We could make use of a scientific calculator to obtain the trigonometric value of an angle. (Your calculator may work in a slightly different way. Please check your manual.) Example:Find the value of cos 6.35˚. Solution:Press <cos 6.35˚ = 0.9939 (correct to 4 decimal places) Example:Find the value of sin 40˚ 32’. Solution: sin 40˚… Continue reading How To Use A Calculator To Find Trig Ratios And Angles?
Find exact values of expressions involving sin, cos and tan
Find exact values of expressions involving sine, cosine and tangent values of 0, 30, 45, 60 and 90 degrees Example:Determine the exact values of each of the following:a) sin30°tan45° + tan30°sin60°b) cos30°sin45° + sin30°tan30°
How to find the trig ratios of the special angles?
Using a 45-45-90 triangle and a 30-60-90 triangle find sine, cosine and tangent values of 0, 30, 45, 60 and 90 degrees
Special Angles
We will first look into the trigonometric functions of the angles 30°, 45° and 60°. Let us consider 30° and 60°. These two angles form a 30°-60°-90° right triangle as shown. The ratio of the sides of the triangle is1 : √3 : 2 From the triangle we get the ratios as follows: Next, we… Continue reading Special Angles