Retake: Unit 3 Laws, Area, and Trig Identities

Front

What is the formula for the area of a triangle given two sides and the included angle?

Back

Area = \frac{1}{2}ab \sin(C), where a and b are the lengths of the sides and C is the included angle.

Front

Simplify: tanB (cotB + tanB)

Back

sec^2 B

Front

What is the relationship between secant and cosine?

Back

sec(x) = \frac{1}{cos(x)}.

Front

What is the area of a triangle with sides 5 cm and 8 cm and an included angle of 39°?

Back

12.6 cm²

Front

What is the double-angle identity for tangent?

Back

tan(2θ) = \frac{2tan(θ)}{1 - tan^2(θ).

Front

Calculate the area of a triangle with a base of 10 m and a height of 6 m.

Back

Area = \frac{1}{2} \times base \times height = 30 m².

Front

What is the formula for the area of a triangle using Heron's formula?

Back

Area = \sqrt{s(s-a)(s-b)(s-c)}, where s = \frac{(a+b+c)}{2}.

Front

If sin θ = -\frac{3}{5}, what is cos θ in the fourth quadrant?

Back

cos θ = \frac{4}{5}.

Front

What is the value of tan(2θ) if sin θ = -\frac{3}{5}?

Back

tan(2θ) = -\frac{24}{7}.

Front

What is the Pythagorean identity for sine and cosine?

Back

sin^2(x) + cos^2(x) = 1.