Trigonometr

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

This topic covers the skill of calculating angles from given trigonometric ratios using inverse trigonometric functions, expressed in negative one notation (such as \( \cos^{-1} \), \( \tan^{-1} \), etc.). Each problem provides a ratio for a trigonometric function (cosine or tangent) and asks students to find the corresponding angle utilizing the inverse of that function. The multiple-choice format presents variations on how to apply inverse trigonometric functions and manipulate expressions to calculate angles correctly. Such practice is instrumental in deepening understanding of trigonometry fundamentals.

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

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Calculating Angles from Ratios (to -1 Notation)

Complete these online problems with 80% or 4 correct answers in a row. Results are immediate.

How would you calculate the angle, using -1 notation?

\text{cos}(\alpha) = 0.961

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

Math worksheet on 'Trigonometry - Calculating Angles from Ratios (to -1 Notation) (Level 1)'. Part of a broader unit on 'Trigonometry Fundamentals - Intro' Learn online: app.mobius.academy/math/units/trigonometry_fundamentals_intro/

How would you calculate the angle, using -1 notation?

$A LaTex expression showing \text{cos}(\alpha) = 0.743$

a $A LaTex expression showing \alpha = 1 over \text{acos (0.743)}$

b $A LaTex expression showing \alpha = \text{cos}(0.743) - 1$

c $A LaTex expression showing \alpha = 1 over \text{cos to the power of -1 (0.743)}$

d $A LaTex expression showing \alpha = \text{cos} to the power of -1 (0.743)$

How would you calculate the angle, using -1 notation?

$A LaTex expression showing \text{tan}(\alpha) = 5.671$

a $A LaTex expression showing \alpha = \text{tan}(5.671) - 1$

b $A LaTex expression showing \alpha = \text{tan} to the power of -1 (5.671)$

c $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (5.671)}$

d $A LaTex expression showing \alpha = 1 over \text{atan (5.671)}$

How would you calculate the angle, using -1 notation?

$A LaTex expression showing \text{tan}(\alpha) = 1.111$

a $A LaTex expression showing \alpha = 1 over \text{atan (1.111)}$

b $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (1.111)}$

c $A LaTex expression showing \alpha = \text{tan}(1.111) - 1$

d $A LaTex expression showing \alpha = \text{tan} to the power of -1 (1.111)$

How would you calculate the angle, using -1 notation?

$A LaTex expression showing \text{tan}(\alpha) = 9.514$

a $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (9.514)}$

b $A LaTex expression showing \alpha = \text{tan}(9.514) - 1$

c $A LaTex expression showing \alpha = \text{tan} to the power of -1 (9.514)$

d $A LaTex expression showing \alpha = 1 over \text{atan (9.514)}$

How would you calculate the angle, using -1 notation?

$A LaTex expression showing \text{tan}(\alpha) = 4.705$

a $A LaTex expression showing \alpha = \text{tan}(4.705) - 1$

b $A LaTex expression showing \alpha = \text{tan} to the power of -1 (4.705)$

c $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (4.705)}$

d $A LaTex expression showing \alpha = 1 over \text{atan (4.705)}$

How would you calculate the angle, using -1 notation?

$A LaTex expression showing \text{cos}(\alpha) = 0.545$

a $A LaTex expression showing \alpha = \text{cos}(0.545) - 1$

b $A LaTex expression showing \alpha = \text{cos} to the power of -1 (0.545)$

c $A LaTex expression showing \alpha = 1 over \text{cos to the power of -1 (0.545)}$

d $A LaTex expression showing \alpha = 1 over \text{acos (0.545)}$

How would you calculate the angle, using -1 notation?

$A LaTex expression showing \text{cos}(\alpha) = 0.961$

a $A LaTex expression showing \alpha = \text{cos}(0.961) - 1$

b $A LaTex expression showing \alpha = \text{cos} to the power of -1 (0.961)$

c $A LaTex expression showing \alpha = 1 over \text{cos to the power of -1 (0.961)}$

d $A LaTex expression showing \alpha = 1 over \text{acos (0.961)}$