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

The math topic focuses on calculating angles from given trigonometric ratios using the inverse functions (notated as -1, i.e., arcsin, arccos, arctan). Various problems require identifying the angle, denoted by alpha (α), from specified trigonometric values, such as tangent and cosine. These problems are structured in multiple-choice format, where each problem has several options presenting different angles in degrees. The overall aim is to strengthen understanding and application of inverse trigonometric functions to solve for angles when trigonometric ratios are given. This forms an introductory part of basic trigonometric fundamentals.

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

Calculating Angles from Ratios (-1 Notation)

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Calculate the angle in degrees, given the trigonometric ratio

\text{sin}^{-1}(0.99) = \alpha

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

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

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{tan} to the power of -1 (0.554) = \alpha$

a $A LaTex expression showing \alpha=34 to the power of circle$

b $A LaTex expression showing \alpha=24 to the power of circle$

c $A LaTex expression showing \alpha=9 to the power of circle$

d $A LaTex expression showing \alpha=29 to the power of circle$

e $A LaTex expression showing \alpha=14 to the power of circle$

f $A LaTex expression showing \alpha=39 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{tan} to the power of -1 (2.145) = \alpha$

a $A LaTex expression showing \alpha=60 to the power of circle$

b $A LaTex expression showing \alpha=65 to the power of circle$

c $A LaTex expression showing \alpha=50 to the power of circle$

d $A LaTex expression showing \alpha=55 to the power of circle$

e $A LaTex expression showing \alpha=80 to the power of circle$

f $A LaTex expression showing \alpha=75 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{cos} to the power of -1 (0.809) = \alpha$

a $A LaTex expression showing \alpha=56 to the power of circle$

b $A LaTex expression showing \alpha=46 to the power of circle$

c $A LaTex expression showing \alpha=16 to the power of circle$

d $A LaTex expression showing \alpha=36 to the power of circle$

e $A LaTex expression showing \alpha=51 to the power of circle$

f $A LaTex expression showing \alpha=21 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{tan} to the power of -1 (0.869) = \alpha$

a $A LaTex expression showing \alpha=26 to the power of circle$

b $A LaTex expression showing \alpha=61 to the power of circle$

c $A LaTex expression showing \alpha=41 to the power of circle$

d $A LaTex expression showing \alpha=51 to the power of circle$

e $A LaTex expression showing \alpha=21 to the power of circle$

f $A LaTex expression showing \alpha=31 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{tan} to the power of -1 (0.404) = \alpha$

a $A LaTex expression showing \alpha=17 to the power of circle$

b $A LaTex expression showing \alpha=22 to the power of circle$

c $A LaTex expression showing \alpha=37 to the power of circle$

d $A LaTex expression showing \alpha=12 to the power of circle$

e $A LaTex expression showing \alpha=27 to the power of circle$

f $A LaTex expression showing \alpha=32 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{tan} to the power of -1 (1.6) = \alpha$

a $A LaTex expression showing \alpha=58 to the power of circle$

b $A LaTex expression showing \alpha=43 to the power of circle$

c $A LaTex expression showing \alpha=53 to the power of circle$

d $A LaTex expression showing \alpha=63 to the power of circle$

e $A LaTex expression showing \alpha=38 to the power of circle$

f $A LaTex expression showing \alpha=48 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{sin} to the power of -1 (0.999) = \alpha$

a $A LaTex expression showing \alpha=103 to the power of circle$

b $A LaTex expression showing \alpha=98 to the power of circle$

c $A LaTex expression showing \alpha=78 to the power of circle$

d $A LaTex expression showing \alpha=93 to the power of circle$

e $A LaTex expression showing \alpha=88 to the power of circle$

f $A LaTex expression showing \alpha=68 to the power of circle$