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Both Answers, Rounded

Part of the Trig Equations and Inverses section of Coddy's Trigonometry journey. Lesson 21 of 52.

$\sin\left(x\right) = 0.2$ is not on the table. The calculator gives one answer, arcsin(0.2) = 11.54° to two places. The circle still has two points at that height, so the second is 180° − 11.54°, which is 168.46°.

$One turn of the sine wave and the dashed line at height 0.2$

The calculator finds the first crossing. The second is its mirror.

On the board, the arcsin chip writes both cases exactly, x = arcsin(0.2) and x = 180° − arcsin(0.2), and you round each one. The calculator's single answer is where students lose the second solution.

Challenge

Solve $4\sin\left(x\right) = 3$ for every x in [0°, 360°), each to two decimal places, and press Check.

Try it yourself

4\sin x = 3

Get $x$ alone $0^{\circ} \le x < 360^{\circ}$

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 Radians An Angle From a Slope Recap: Inverse Values

6Off the Special Angles

Both Answers, RoundedA 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