Henry is asked to find the exact value of cosine StartFraction 10 pi Over 3 EndFraction. His steps are shown below.

1. Subtract 2 pi from StartFraction 10 pi Over 3 EndFraction as many times as possible:

StartFraction 10 pi Over 3 EndFraction – 2 pi = StartFraction 4 pi Over 3 EndFraction

2. Find the reference angle for StartFraction 4 pi Over 3 EndFraction: StartFraction 3 pi Over 2 EndFraction – StartFraction 4 pi Over 3 EndFraction= StartFraction pi Over 6 EndFraction.

3. The cosine value for StartFraction pi Over 6 EndFraction is StartFraction StartRoot 3 EndRoot Over 2 EndFraction.

4. The cosine value is positive because StartFraction pi Over 6 EndFraction is in the first quadrant.

Which of the following describes Henry’s errors?

The reference angle should be StartFraction pi Over 3 EndFraction, and the sign of the value should be negative.

The reference angle should be StartFraction pi Over 3 EndFraction, and the cosine value for StartFraction pi Over 3 EndFraction is One-half.

The sign of the value should be negative, and the reference angle and quadrant should be determined by subtracting Pi in the first step.

The cosine value for StartFraction pi Over 6 EndFraction is One-half, and the reference angle and quadrant should be determined by subtracting Pi in the first step.
Just wanted to put the answer choice out hereITS as in Apple

Answer: question no. 1 -a. yes, the sides are in the ratio 2 : 5.question no. 2 -b. 59°question no. 3 -c. angles x and y are remote interior angles.question no. 4 -d. 90°, 45° and 45°question no. 5 -b. mn and qrstep-by-step explanation: question no. 1 -rs : xu = 3 : 7.5 = 2 : 5rt : x? = 6.4 : 16 = 2 : 5st : u? = 6 : 15 = 2 : 5as the ratios of all sides are equivalent, the triangles must be congruent and the sides must be proportional.therefore, the answer is: a. yes, the sides are in the ratio 2 : 5.question no. 2 -in the second diagram, angle b is the only letter not shown. therefore, the number must be equivalent to angle b.if we substitute the value of angle b as being 22° in the first diagram, we can now use the angle sum of a triangle to obtain the value of angle a.angle sum of a triangle = 180°therefore: let angle a = aa + 99 + 22 = 180a = 180 - 99 - 22a = 59°therefore, the answer is: b. 59°question no. 3 -angles x and y don't share the vertex of the triangle with the exterior angle w. remote interior angles don't share a vertex of a triangle with an exterior angle. this means that angles x and y are remote interior angles.therefore, the answer is: c. angles x and y are remote interior angles.question no. 4 -the sum of all interior angles of a triangle must be equivalent to 180°.90°, 45° and 45° are the only set of angle measures that are equivalent to 180°.therefore, the answer is: d. 90°, 45° and 45°question no. 5 -the only pair of sides stated in the options which are corresponding are mn and qr.therefore, the answer is: b. mn and qr.