Trigonometr

Calculating Angles from Ratios (Level 1)

This math topic focuses on advanced trigonometry, specifically on calculating angles from given trigonometric ratios. Students are required to find angles in degrees based on values of sine, cosine, and tangent. The problems range from finding angles for basic sine and cosine values to solving for angles using different tangent values. Each question includes multiple-choice answers, enhancing the students' problem-solving skills in interpreting trigonometric ratios to determine angle measures. This is a part of a broader unit on advanced 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

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

Calculate the angle in degrees, given the trigonometric ratio

\text{sin}(\alpha) = 0.616

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Trigonometry - Calculating Angles from Ratios Worksheet

Math worksheet on 'Trigonometry - Calculating Angles from Ratios (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

$A LaTex expression showing \text{cos}(\alpha) = 0.848$

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

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

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

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

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

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

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{cos}(\alpha) = 0.602$

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

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

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

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

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

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

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{sin}(\alpha) = 0.998$

a $A LaTex expression showing \alpha=86 to the power of circle$

b $A LaTex expression showing \alpha=71 to the power of circle$

c $A LaTex expression showing \alpha=106 to the power of circle$

d $A LaTex expression showing \alpha=101 to the power of circle$

e $A LaTex expression showing \alpha=81 to the power of circle$

f $A LaTex expression showing \alpha=96 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{tan}(\alpha) = 0.404$

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

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

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

d $A LaTex expression showing \alpha=7 to the power of circle$

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

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

Calculate the angle in degrees, given the trigonometric ratio

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

a $A LaTex expression showing \alpha=85 to the power of circle$

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

c $A LaTex expression showing \alpha=70 to the power of circle$

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

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

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

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{sin}(\alpha) = 0.342$

a $A LaTex expression showing \alpha=0 to the power of circle$

b $A LaTex expression showing \alpha=25 to the power of circle$

c $A LaTex expression showing \alpha=20 to the power of circle$

d $A LaTex expression showing \alpha=5 to the power of circle$

e $A LaTex expression showing \alpha=10 to the power of circle$

f $A LaTex expression showing \alpha=15 to the power of circle$

Calculate the angle in degrees, given the trigonometric ratio

$A LaTex expression showing \text{tan}(\alpha) = 0.81$

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

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

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

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

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

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