Mathematics
Grade 10
15 min
Inverses of trigonometric functions
Inverses of trigonometric functions
What you'll learn
- Identify the correct order of operations (PEMDAS/BODMAS) in at least 8 out of 10 math problems.
- Solve multi-step math problems involving parentheses, exponents, multiplication, division, addition, and subtraction with 80% accuracy.
- Explain the reasoning behind each step taken when solving a multi-step math problem, using correct mathematical vocabulary, in writing for at least 3 out of 4 problems.
- Apply the order of operations to real-world scenarios presented in word problems and correctly solve them in 2 out of 3 instances.
Tutorial Preview
1
Introduction & Learning Objectives
Learning Objectives
Define the inverse trigonometric functions: arcsine, arccosine, and arctangent.
Correctly use the notation sin⁻¹, cos⁻¹, and tan⁻¹.
Use a scientific calculator to find the measure of an angle given its trigonometric ratio.
Solve for an unknown angle in a right-angled triangle using inverse trigonometric functions.
Distinguish between an inverse trigonometric function (e.g., sin⁻¹(x)) and a reciprocal function (e.g., 1/sin(x)).
Apply inverse trigonometric functions to solve real-world problems involving angles of elevation and depression.
You know how to find the length of a ramp, but how do you find out how steep it is? 🤔 Inverse trig functions give us the answer by helping us find the angle!
So far, you've used SOH CAH TOA to find the length of a...
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Key Concepts & Vocabulary
TermDefinitionExample
Inverse FunctionA function that 'undoes' the action of another function. For example, if a function takes you from A to B, its inverse takes you from B back to A.If f(x) = x + 5, its inverse is f⁻¹(x) = x - 5. If you input 3 into f(x) you get 8. If you input 8 into f⁻¹(x), you get back to 3.
Inverse Sine (Arcsine)The function that 'undoes' sine. If you know the ratio of the opposite side to the hypotenuse, inverse sine tells you the angle.If sin(θ) = 0.5, then θ = sin⁻¹(0.5), which means θ = 30°.
Inverse Cosine (Arccosine)The function that 'undoes' cosine. If you know the ratio of the adjacent side to the hypotenuse, inverse cosine tells you the angle.If cos(θ) = 0.5, then θ = cos⁻¹(0.5), which means θ = 60°.
Inverse Tangent (Arctangent)...
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Core Formulas
Finding an Angle with Sine
If sin(θ) = (Opposite / Hypotenuse), then θ = sin⁻¹(Opposite / Hypotenuse)
Use this when you know the lengths of the side opposite the angle you're looking for and the hypotenuse.
Finding an Angle with Cosine
If cos(θ) = (Adjacent / Hypotenuse), then θ = cos⁻¹(Adjacent / Hypotenuse)
Use this when you know the lengths of the side adjacent to the angle you're looking for and the hypotenuse.
Finding an Angle with Tangent
If tan(θ) = (Opposite / Adjacent), then θ = tan⁻¹(Opposite / Adjacent)
Use this when you know the lengths of the side opposite and the side adjacent to the angle you're looking for.
4 more steps in this tutorial
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Challenging
An isosceles triangle has two equal sides of length 15 cm and a base of 18 cm. Find the measure of the vertex angle (the angle between the two equal sides) to the nearest degree.
A.37°
B.74°
C.53°
D.106°
Challenging
A student is solving for angle θ in a right triangle where the adjacent side is 12 and the hypotenuse is 15. They correctly set up θ = cos⁻¹(12/15) but their calculator displays 0.6435. What is the most likely reason their answer is incorrect for a typical geometry problem?
A.They accidentally calculated sin⁻¹(12/15) instead.
B.Their calculator is in Radian (RAD) mode instead of Degree (DEG) mode.
C.They should have calculated cos⁻¹(15/12).
D.They typed 'cos' instead of 'cos⁻¹'.
Challenging
A rectangle has a length of 20 cm and a diagonal of 25 cm. What is the angle that the diagonal makes with the shorter side of the rectangle? Round to the nearest degree.
A.37°
B.53°
C.39°
D.51°
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What grade level is "Inverses of trigonometric functions"?
Inverses of trigonometric functions is a Grade 10 Mathematics lesson on ExcelOS.
What will I learn in Inverses of trigonometric functions?
You'll be able to: Identify the correct order of operations (PEMDAS/BODMAS) in at least 8 out of 10 math problems; Solve multi-step math problems involving parentheses, exponents, multiplication, division, addition, and subtraction with 80%….
Is "Inverses of trigonometric functions" free to practice?
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How many practice questions are included with Inverses of trigonometric functions?
This lesson includes 25 practice questions across multiple difficulty levels, each with instant feedback and explanations.