Trigonometr

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

This math topic focuses on using trigonometric functions to calculate angles from given ratios, primarily using inverse trigonometric functions (arc functions). It covers problems involving the sine (sin), cosine (cos), and tangent (tan) functions, converting specific ratios to angles using arc notation like arcsine (asin), arccosine (acos), and arctangent (atan). Each question in the series offers multiple choices to identify the correct application of these functions, reinforcing understanding of how to correctly interpret trigonometric ratios and calculate corresponding angles.

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

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Calculating Angles from Ratios (to Arc Notation)

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

How would you calculate the angle, using arc notation?

\text{tan}(\alpha) = 2.05

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

Math worksheet on 'Trigonometry - Calculating Angles from Ratios (to Arc 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 arc notation?

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

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

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

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

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

How would you calculate the angle, using arc notation?

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

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

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

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

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

How would you calculate the angle, using arc notation?

$A LaTex expression showing \text{sin}(\alpha) = 0.259$

a $A LaTex expression showing \alpha = \text{sin}(0.259) - 1$

b $A LaTex expression showing \alpha = 1 over \text{sin to the power of -1 (0.259)}$

c $A LaTex expression showing \alpha = \text{asin}(0.259)$

d $A LaTex expression showing \alpha = 1 over \text{asin (0.259)}$

How would you calculate the angle, using arc notation?

$A LaTex expression showing \text{cos}(\alpha) = 0.921$

a $A LaTex expression showing \alpha = \text{acos}(0.921)$

b $A LaTex expression showing \alpha = 1 over \text{cos to the power of -1 (0.921)}$

c $A LaTex expression showing \alpha = 1 over \text{acos (0.921)}$

d $A LaTex expression showing \alpha = \text{cos}(0.921) - 1$

How would you calculate the angle, using arc notation?

$A LaTex expression showing \text{tan}(\alpha) = 0.306$

a $A LaTex expression showing \alpha = \text{tan}(0.306) - 1$

b $A LaTex expression showing \alpha = 1 over \text{tan to the power of -1 (0.306)}$

c $A LaTex expression showing \alpha = \text{atan}(0.306)$

d $A LaTex expression showing \alpha = 1 over \text{atan (0.306)}$

How would you calculate the angle, using arc notation?

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

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

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

c $A LaTex expression showing \alpha = \text{atan}(1.28)$

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

How would you calculate the angle, using arc notation?

$A LaTex expression showing \text{sin}(\alpha) = 0.656$

a $A LaTex expression showing \alpha = \text{asin}(0.656)$

b $A LaTex expression showing \alpha = \text{sin}(0.656) - 1$

c $A LaTex expression showing \alpha = 1 over \text{asin (0.656)}$

d $A LaTex expression showing \alpha = 1 over \text{sin to the power of -1 (0.656)}$