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

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

This math topic focuses on trigonometry, specifically how to calculate angles from given trigonometric ratios using inverse notation (indicated by -1). The problems involve presenting a trigonometric function value (cosine, sine, or tangent) and asking the learner to determine the corresponding angle using inverse trigonometric functions, which is represented in various mathematical expressions as answers.

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 -1 Notation) Worksheet

Trigonometry - Calculating Angles from Ratios (Words to -1 Notation)

How would you calculate the angle using -1 notation?

$A LaTex expression showing \alpha\text{ has a tan of }1.28$

a $A LaTex expression showing \alpha = \text{tan}(1.28) - 1$

b $A LaTex expression showing \alpha = \text{tan} to the power of -1 (1.28)$

c $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (1.28)}$

d $A LaTex expression showing \alpha = 1 over \text{atan (1.28)}$

How would you calculate the angle using -1 notation?

$A LaTex expression showing \alpha\text{ has a tan of }5.145$

a $A LaTex expression showing \alpha = \text{tan}(5.145) - 1$

b $A LaTex expression showing \alpha = \text{tan} to the power of -1 (5.145)$

c $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (5.145)}$

d $A LaTex expression showing \alpha = 1 over \text{atan (5.145)}$

How would you calculate the angle using -1 notation?

$A LaTex expression showing \alpha\text{ has a tan of }0.966$

a $A LaTex expression showing \alpha = \text{tan}(0.966) - 1$

b $A LaTex expression showing \alpha = 1 over \text{atan (0.966)}$

c $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (0.966)}$

d $A LaTex expression showing \alpha = \text{tan} to the power of -1 (0.966)$

How would you calculate the angle using -1 notation?

$A LaTex expression showing \alpha\text{ has a sin of }0.988$

a $A LaTex expression showing \alpha = \text{sin} to the power of -1 (0.988)$

b $A LaTex expression showing \alpha = \text{sin}(0.988) - 1$

c $A LaTex expression showing \alpha = 1 over \text{sin to the power of -1 (0.988)}$

d $A LaTex expression showing \alpha = 1 over \text{asin (0.988)}$

How would you calculate the angle using -1 notation?

$A LaTex expression showing \alpha\text{ has a sin of }0.276$

a $A LaTex expression showing \alpha = \text{sin} to the power of -1 (0.276)$

b $A LaTex expression showing \alpha = 1 over \text{sin to the power of -1 (0.276)}$

c $A LaTex expression showing \alpha = \text{sin}(0.276) - 1$

d $A LaTex expression showing \alpha = 1 over \text{asin (0.276)}$

How would you calculate the angle using -1 notation?

$A LaTex expression showing \alpha\text{ has a tan of }6.314$

a $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (6.314)}$

b $A LaTex expression showing \alpha = \text{tan}(6.314) - 1$

c $A LaTex expression showing \alpha = 1 over \text{atan (6.314)}$

d $A LaTex expression showing \alpha = \text{tan} to the power of -1 (6.314)$

How would you calculate the angle using -1 notation?

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

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

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

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

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

How would you calculate the angle using -1 notation?

$A LaTex expression showing \alpha\text{ has a tan of }0.231$

a $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (0.231)}$

b $A LaTex expression showing \alpha = \text{tan} to the power of -1 (0.231)$

c $A LaTex expression showing \alpha = 1 over \text{atan (0.231)}$

d $A LaTex expression showing \alpha = \text{tan}(0.231) - 1$