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Rounded Angles in Radians

Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 8 of 52.

Two friends work out $\arccos\left(-0.8\right)$ . One gets 143.13, the other 2.50. Who is right?

Both are right. 143.13° and 2.50 radians are the same angle. A calculator in DEG mode answers in degrees. In RAD mode it answers in radians. So check the mode first. Round only once, at the end. A quick check: arccos of a negative number is more than 90°, which is about 1.57 radians.

Challenge

A seat on a big wheel of radius 10 m starts level with the hub, on the right, and goes up. When it is 3 m left of the hub, it has turned through $x = \arccos\left(-0.3\right)$ radians. Work out x to two decimal places. Write x ≈ … as the next line. Done means x is a number of radians with 2 decimals.

Then press Check.

Try it yourself

x = \arccos\left(-0.3\right)

Get $x$ alone

All lessons in Trig Equations and Inverses

1Your First Trig Equations

One Equation, Two Angles Reading Signs on the Circle Recap: First Equations

4Compositions

Draw the Triangle The Outer Function A Negative Inside When Undoing Does Not Undo Recap: Compositions

7General Solutions

Every Solution Tangent's Single Family Families in Radians Families, Rounded Recap: Every Solution

10Identities First

Write sin 2x Out Pick the Right cos 2x Swap cos²x for sin²x sec, csc and cot Recap: Identities First

2Inverses and Their Ranges

Why arcsin Gives One Angle The Range of arccos The Range of arctan Recap: Inverse Ranges

5Equations on a Domain

A Negative Cosine Tangent Equations Equations in Radians Two Turns, Four Answers Recap: On a Domain

8Multiple Angles

Two Turns for 2x Solving sin 2x Half Angles Every Solution of sin 3x Recap: Multiple Angles

11Final Challenges

Final: The Bicycle Pedal Final: The Big Wheel Final: Every Solution Final: An Identity and More Final: An Inverse Inside

3Evaluating Inverse Trig

Rounded Angles in RadiansAn Angle From a Slope Recap: Inverse Values

6Off the Special Angles

Both Answers, Rounded A Negative Sine, Rounded Cosine, Rounded Tangent, Rounded Rounded, in Radians Recap: Off the Table

9Factoring Trig Equations

A Common Factor Never Divide by sin x A Quadratic in Sine A Case With No Angle Square Roots Give Two Signs Recap: Factoring