sin²θ + cos²θ = 1, and tan θ = sin θ / cos θ. Those two identities are the ACT's extra trig beyond SOH-CAH-TOA. If a question gives you sine and asks for cosine, square the sine, subtract from 1, and take a square root. Right-triangle ratios are in SOH-CAH-TOA.
When to use it
You know sin θ = 3/5. Then cos²θ = 1 − 9/25 = 16/25, so cos θ is 4/5 or −4/5. On a right triangle in the first quadrant, take the positive value. tan θ is then (3/5) / (4/5) = 3/4, which is also opposite over adjacent.
Reciprocals — csc, sec, cot — are 1 over sin, cos, and tan. They are rare. Draw the triangle if you have two sides. The trig pillar is right-triangle trigonometry.
The bottom line
Squares of sine and cosine add to 1. Tangent is sine over cosine. If you already have two sides, skip the identity and use the ratio. The formula list is in ACT Math formulas.
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