SAT-Style Trig Practice Set Part 2

10. SAT-Style Coordinate Geometry Trig (Medium-Hard)

*Watch this video:

Visual

Draw:

• coordinate plane
• point at (3,4)
• triangle from origin to point

If the segment from the origin to (3,4) forms angle $\theta$ with the x-axis, find:

• $\sin\theta$
• $\cos\theta$
• $\tan\theta$

11. Rotation & Quadrants (Medium-Hard)

If:

• cosine is negative
• sine is positive

which quadrant could the angle be in?

12. Special Triangle Recognition (Medium-Hard)

Visual

Draw:

30-60-90 triangle:

• short leg = 5

Find:

• long leg
• hypotenuse
• $\sin(30^\circ)$
• $\cos(30^\circ)$

13. SAT Trap — Tangent as Slope (Hard)

Visual

Draw:

• line through origin
• point (4,2)

Question:

If the line forms angle $\theta$ with the x-axis, what is $\tan(\theta)$ ?

14. Extrapolation Question (Hard but Conceptual)

Visual

Draw:

• coordinate plane
• point rotating around a circle
• start at (1,0)
• rotate counterclockwise $90^\circ$

Predict the new coordinate point.

What are:

• cosine
• sine

15. Real-World Navigation Question (Harder Conceptual)

Why might engineers use triangles and angles to estimate the location of satellites or GPS signals?

A. Because the Earth is flat, so triangles are the simplest way to measure straight distances.

B. Because using triangles and angles allows engineers to calculate unknown distances and positions based on known measurements, even on a curved surface like Earth.

C. Because satellites always send signals in the shape of triangles to Earth.

D. Because angles are easier to measure than distances, so no other information is needed.