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

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

This math topic focuses on calculating angles from trigonometric ratios, specifically using the inverse trigonometric functions: arcsine (asin), arctangent (atan), and arccosine (acos). The problems present various trigonometric ratios, and learners must calculate corresponding degrees. Options for each question are given in multiple-choice format. This is part of an introductory unit on trigonometry fundamentals, which teaches how to interpret arc notation and trigonometric calculations. The goal is to enhance understanding of trigonometric relationships and angle calculations.

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

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Trigonometry - Calculating Angles from Ratios (Arc Notation) Worksheet

Trigonometry - Calculating Angles from Ratios (Arc Notation)

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{acos}(0.174) = \alpha$

a $A LaTex expression showing \alpha=100 to the power of circle$

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

c $A LaTex expression showing \alpha=90 to the power of circle$

d $A LaTex expression showing \alpha=95 to the power of circle$

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

$A LaTex expression showing \text{atan}(19.081) = \alpha$

a $A LaTex expression showing \alpha=92 to the power of circle$

b $A LaTex expression showing \alpha=97 to the power of circle$

c $A LaTex expression showing \alpha=107 to the power of circle$

d $A LaTex expression showing \alpha=87 to the power of circle$

e $A LaTex expression showing \alpha=102 to the power of circle$

f $A LaTex expression showing \alpha=82 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{atan}(3.271) = \alpha$

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

b $A LaTex expression showing \alpha=83 to the power of circle$

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

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

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

f $A LaTex expression showing \alpha=73 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{acos}(0.788) = \alpha$

a $A LaTex expression showing \alpha=28 to the power of circle$

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

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

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

e $A LaTex expression showing \alpha=33 to the power of circle$

f $A LaTex expression showing \alpha=23 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{asin}(0.469) = \alpha$

a $A LaTex expression showing \alpha=8 to the power of circle$

b $A LaTex expression showing \alpha=33 to the power of circle$

c $A LaTex expression showing \alpha=13 to the power of circle$

d $A LaTex expression showing \alpha=23 to the power of circle$

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

f $A LaTex expression showing \alpha=28 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{acos}(0.052) = \alpha$

a $A LaTex expression showing \alpha=77 to the power of circle$

b $A LaTex expression showing \alpha=87 to the power of circle$

c $A LaTex expression showing \alpha=97 to the power of circle$

d $A LaTex expression showing \alpha=92 to the power of circle$

e $A LaTex expression showing \alpha=107 to the power of circle$

f $A LaTex expression showing \alpha=67 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{asin}(0.883) = \alpha$

a $A LaTex expression showing \alpha=52 to the power of circle$

b $A LaTex expression showing \alpha=42 to the power of circle$

c $A LaTex expression showing \alpha=82 to the power of circle$

d $A LaTex expression showing \alpha=47 to the power of circle$

e $A LaTex expression showing \alpha=72 to the power of circle$

f $A LaTex expression showing \alpha=62 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{asin}(0.857) = \alpha$

a $A LaTex expression showing \alpha=54 to the power of circle$

b $A LaTex expression showing \alpha=49 to the power of circle$

c $A LaTex expression showing \alpha=74 to the power of circle$

d $A LaTex expression showing \alpha=44 to the power of circle$

e $A LaTex expression showing \alpha=69 to the power of circle$

f $A LaTex expression showing \alpha=59 to the power of circle$