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θ Trigonometry Explorer
45°
= π/4 rad
sin θ0.7071
cos θ0.7071
tan θ1.0000
Quadrant I — sin+, cos+, tan+
+=
=
=
Eq 1:x+=x+
Eq 1:x+y=
Eq 2:x+y=
Apply to BOTH sides:
Target:
Combine (elimination):
Substitution:
Solve one equation for x or y first.
Steps will appear here as you solve…
🎉 Well done!
x²+
x+
=0
Your Working
Identify a, b, and c, then calculate the discriminant:
Discriminant: b² − 4ac =
Solutions: x =
Full Solution
Why ± ?
■ Opposite (O)
■ Adjacent (A)
■ Hypotenuse (H)
Problem Setup
°
Step 1: Label the sides
Relative to the angle θ, which side is which?
Opposite:
Adjacent:
Hypotenuse:
Step 2: Choose the ratio
Which trig ratio uses the sides you have and need?
Step 3: Solve
Enter your answer:
SOHCAHTOA — The Three Ratios
In a right-angled triangle, the three trigonometric ratios connect an angle to the lengths of two sides. The mnemonic SOH-CAH-TOA helps you remember which ratio to use.
SOH — Sine
Use when you have or need the Opposite and Hypotenuse.
CAH — Cosine
Use when you have or need the Adjacent and Hypotenuse.
TOA — Tangent
Use when you have or need the Opposite and Adjacent.
How to use:
- Label the sides relative to the angle θ — which is opposite, adjacent, and the hypotenuse?
- Choose the ratio that connects the side you know with the side you need.
- Substitute the known values into the formula.
- Rearrange and solve for the unknown.
Fraction Arithmetic
=
Step-by-step Solution
∠ Angle Relationships
Adjust the angle
1°
89°
Angle α
55°
Complement
35°
Two angles that add up to 90°
55° + 35° = 90°
Formatted Equation
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Result
1
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