# Cosine control on trigonometry in 4th grade.

The chapter on cosine is very interesting but also important. To check students’ understanding, a math test in the fourth grade on trigonometry in the triangle and the cosine (cos ) of an acute angle is necessary. During this evaluation, the teacher will have the opportunity to check if the students have assimilated the course.

## Cosine control

### Exercise 1 (3 points)

Solve each of the following equations:

a) 8 + x = – 4

b) 5 x – 6 = 10

c)

### Exercise 2 (2 points)

What number must be added to the numerator and denominator of to obtain the fraction ?

### Exercise 3 (3,5points) ‘the cosine’.

ABC is a right triangle at A.

a) Make a full-scale figure and plot the data on it,

b) Calculate an approximate value of the length AB rounded to the hundredth .

BC = 10 cm = 36°.

c) calculate the length AC .

### Exercise 4 (1,5points) ‘the cosine’.

DEF is a right triangle in D

Make a freehand figure.

We have. DE = 8 cm = 31° Calculate EF.

### Exercise 5 (3 points)

a)Prove that triangle ABC is a rectangle. specify in which point.

We have: AB = 30 cm AC = 12.5 cm BC = 32.5 cm.

b) Calculate cos .

Deduce a value of the angle to the nearest degree.

### Exercise 6 (3 points)

The length x of a rectangle, in centimeters, exceeds its width by 4 cm.

a) Write its width as a function of x.

b) Write the perimeter of this rectangle as a function of x.

c) Calculate x when this perimeter measures 140 cm.

### Exercise 7 (4points)

In a pastry shop, a custard tart is sold in slices.

This is the price of one share.

After having sold 3.80 €, there are 5 shares left.

After having sold 5 €, there are 4 shares left.

1. Reproduce and complete the equality :

5 x + 3,80 = …………

which translates the price of a pie in two ways.

2. Solve the resulting equation to determine the price of a unit.

3. Calculate the number of slices that can be made in a pie.

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