Trigonometry - Calculating Angles from Ratios (Words to Arc Notation) (Level 1) - Mobius Math Academy

Calculating Angles from Ratios (Words to Arc Notation) (Level 1)

This math topic focuses on calculating angles using trigonometric ratios, specifically transitioning from word descriptions to arc notation. It explores fundamental trigonometry concepts, providing multiple choice questions that ask how to compute an angle given its sine, cosine, or tangent value. The questions also test the understanding of inverse trigonometric functions, such as arcsin, arccos, and arctan, to find angle measures from given trigonometric ratios. This topic is part of an introductory unit on trigonometry fundamentals.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry - Calculating Angles from Ratios (Words to Arc Notation) Worksheet

Trigonometry - Calculating Angles from Ratios (Words to Arc Notation)

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a sin of }0.995$

a $A LaTex expression showing \alpha = \text{sin}(0.995) - 1$

b $A LaTex expression showing \alpha = 1 over \text{asin (0.995)}$

c $A LaTex expression showing \alpha = 1 over \text{sin to the power of -1 (0.995)}$

d $A LaTex expression showing \alpha = \text{asin}(0.995)$

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a cos of }0.946$

a $A LaTex expression showing \alpha = \text{cos}(0.946) - 1$

b $A LaTex expression showing \alpha = 1 over \text{acos (0.946)}$

c $A LaTex expression showing \alpha = \text{acos}(0.946)$

d $A LaTex expression showing \alpha = 1 over \text{cos to the power of -1 (0.946)}$

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a cos of }0.5$

a $A LaTex expression showing \alpha = 1 over \text{acos (0.5)}$

b $A LaTex expression showing \alpha = 1 over \text{cos to the power of -1 (0.5)}$

c $A LaTex expression showing \alpha = \text{acos}(0.5)$

d $A LaTex expression showing \alpha = \text{cos}(0.5) - 1$

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a tan of }1.963$

a $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (1.963)}$

b $A LaTex expression showing \alpha = \text{tan}(1.963) - 1$

c $A LaTex expression showing \alpha = 1 over \text{atan (1.963)}$

d $A LaTex expression showing \alpha = \text{atan}(1.963)$

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a tan of }1.235$

a $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (1.235)}$

b $A LaTex expression showing \alpha = 1 over \text{atan (1.235)}$

c $A LaTex expression showing \alpha = \text{atan}(1.235)$

d $A LaTex expression showing \alpha = \text{tan}(1.235) - 1$

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a sin of }0.777$

a $A LaTex expression showing \alpha = 1 over \text{sin to the power of -1 (0.777)}$

b $A LaTex expression showing \alpha = \text{sin}(0.777) - 1$

c $A LaTex expression showing \alpha = \text{asin}(0.777)$

d $A LaTex expression showing \alpha = 1 over \text{asin (0.777)}$

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a cos of }0.875$

a $A LaTex expression showing \alpha = \text{acos}(0.875)$

b $A LaTex expression showing \alpha = \text{cos}(0.875) - 1$

c $A LaTex expression showing \alpha = 1 over \text{cos to the power of -1 (0.875)}$

d $A LaTex expression showing \alpha = 1 over \text{acos (0.875)}$

How would you calculate the angle using arc notation?

$A LaTex expression showing \alpha\text{ has a sin of }0.819$

a $A LaTex expression showing \alpha = \text{sin}(0.819) - 1$

b $A LaTex expression showing \alpha = 1 over \text{sin to the power of -1 (0.819)}$

c $A LaTex expression showing \alpha = 1 over \text{asin (0.819)}$

d $A LaTex expression showing \alpha = \text{asin}(0.819)$