# Siap Ukk Matematika Wajib Kelas X Sma

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Materi:  Trigonometri

• 1.

### Type description here

• 2.

• 3.

• A.

37,50º

• B.

66,67º

• C.

72,50º

• D.

72º

• E.

75º

E. 75º
Explanation
The correct answer is 75º because when we convert 5/24 of a full rotation into degrees, we multiply it by 360 (the number of degrees in a full rotation) and divide it by 1 (since 5/24 is already in the form of a fraction). This calculation gives us 75º.

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• 4.

• A.

• B.

• C.

• D.

• E.

Explanation
The correct answer is 7/5 π rad. This is because 7/10 of a full rotation is equivalent to 7/10 of 2π radians. Simplifying this gives us 7/5 π radians.

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• 5.

• A.

150º

• B.

135º

• C.

120º

• D.

115º

• E.

105º

B. 135º
Explanation
The correct answer is 135º because when converting radians to degrees, we multiply the radian measure by 180/π. In this case, ¾π rad is equal to (3/4) * (180/π) ≈ 135º.

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• 6.

• A.

-41/9

• B.

-40/41

• C.

-41/40

• D.

41/40

• E.

41/9

D. 41/40
Explanation
The value of sec ∝ is the reciprocal of cos ∝. Since sin ∝ = -9/41, we can determine the value of cos ∝ using the Pythagorean identity sin^2 ∝ + cos^2 ∝ = 1. Plugging in the given value of sin ∝, we get (-9/41)^2 + cos^2 ∝ = 1. Solving for cos ∝, we find that cos ∝ = 40/41. Therefore, the value of sec ∝ is the reciprocal of cos ∝, which is 41/40.

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• 7.

• A.

K III, √3

• B.

K III, √3/3

• C.

K IV, -√3/3

• D.

K IV, -√3

• E.

K IV, 1/3√3

C. K IV, -√3/3
Explanation
The correct answer is K IV, -√3/3.

In trigonometry, the value of the tangent function is negative in the fourth quadrant (K IV). Since the angle is 690 degrees, which is equivalent to 30 degrees past the 4th quadrant, we can use the reference angle of 30 degrees in the first quadrant. The tangent of 30 degrees is √3/3. However, since the angle is in the fourth quadrant, the value is negative. Therefore, the correct answer is K IV, -√3/3.

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• 8.

### Jika β sudut lancip, cos β=4/5 maka tan 2β = ....

• A.

• B.

24/14

• C.

19/14

• D.

11/9

• E.

11/6

Explanation
If β is an acute angle and cos β = 4/5, we can use the double angle formula for tangent to find tan 2β. The formula states that tan 2β = (2tan β)/(1-tan^2 β). Since cos β = 4/5, we can use the Pythagorean identity sin^2 β + cos^2 β = 1 to find sin β = 3/5. Using the formula, we get tan 2β = (2(3/5))/(1-(3/5)^2) = 6/4 = 3/2. Therefore, the correct answer is 24/7.

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• 9.

### Nilai trigonometri dari tan 315º - cos 135º adalah ....

• A.

-3/2 √2

• B.

-1/2 √2

• C.

1/2 √2

• D.

√2

• E.

3/2 √2

B. -1/2 √2
Explanation
The question asks for the trigonometric value of tan 315° - cos 135°. To find this value, we can use the unit circle.

First, we find the reference angle for 315°, which is 45°. The tangent of 45° is 1.

Next, we find the reference angle for 135°, which is 45°. The cosine of 45° is 1/√2.

Substituting these values into the expression, tan 315° - cos 135°, we get 1 - 1/√2. Rationalizing the denominator, this simplifies to (√2 - 1)/√2.

Therefore, the correct answer is -1/2 √2.

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• 10.

### Bentuk ekuivalen dari Sin2A - Cos2A adalah….

• A.

Option 1

• B.

Option 2

• C.

Option 3

• D.

-1

• E.

1

A. Option 1
Explanation
The equivalent form of Sin2A - Cos2A is Option 1.

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• 11.

### Perhatikan rumus relasi kuadrat berikut:i. tan2a - 1 = sec2aii. sin2a + cos2a = 1iii. cotan2a + 1 = cosec2aiv. sec2a - 1 = tan2av. cos2a – sin2a = 1Rumus relasi kuadrat yang tepat ditunjukkan oleh nomor ....

• A.

I, ii, iii

• B.

I, ii, iv

• C.

I, iii, v

• D.

Ii, iii, iv

• E.

Ii, iii, v

D. Ii, iii, iv
Explanation
The correct answer is ii, iii, iv. The formula sin2a + cos2a = 1 represents the Pythagorean identity, which states that the square of the sine of an angle plus the square of the cosine of the same angle is always equal to 1. The formula cotan2a + 1 = cosec2a represents the relationship between the cotangent and cosecant functions. And the formula sec2a - 1 = tan2a represents the relationship between the secant and tangent functions.

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• 12.

### Nilai trigonometri dari sin 105º adalah ....

• A.

1/2(-√2-√3)

• B.

1/2(√6-√2)

• C.

1/4(√6+√2)

• D.

1/4(-√6-√2)

• E.

1/6(√2-√3)

C. 1/4(√6+√2)
Explanation
The correct answer is 1/4(√6+√2). The trigonometric value of sin 105° can be found by using the sum-to-product formula for sine. sin(105°) = sin(60° + 45°) = sin(60°)cos(45°) + cos(60°)sin(45°) = (√3/2)(√2/2) + (1/2)(√2/2) = (√6+√2)/4.

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• 13.

### Nilai sin x pada fungsi trigonometri yang bernilai sama adalah ....

• A.

0º, 90º, 270º

• B.

0º, 180º, 360º

• C.

30º, 150º, 210º

• D.

45º, 135º, 315º

• E.

60º, 120º, 330º

B. 0º, 180º, 360º
Explanation
The given correct answer is 0º, 180º, 360º. This is because the sine function has a periodicity of 360º, meaning that it repeats itself every 360º. The sine function is equal to 0º at 0º, 180º, and 360º, as the sine of these angles is 0. Therefore, these angles have the same sine value.

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• 14.

### Sudut yang memuat nilai maksimum dan minimum fungsi trigonometri f(x) = sin x  adalah ....

• A.

90º, 270º

• B.

45º, 215º

• C.

30º, 150º

• D.

30º, 135º

• E.

0º, 90º

A. 90º, 270º
Explanation
The angles that contain the maximum and minimum values of the trigonometric function f(x) = sin x are 90º and 270º. This is because the sine function reaches its maximum value of 1 at 90º and its minimum value of -1 at 270º.

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• 15.

### Diketahui ∆PQR mempunyai panjang PQ = 464 cm,

• A.

464√3 cm

• B.

464 cm

• C.

332√3 cm

• D.

232√2 cm

• E.

232 cm

B. 464 cm
Explanation
The given answer, 464 cm, is the correct answer because it matches the given information that the length of PQ in triangle PQR is 464 cm.

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• 16.

### Diketahui ∆ABC mempunyai panjang BC = 10 cm, AC = 16 cm, dan <ACB= 60º. Panjang AB adalah ....

• A.

14 cm

• B.

16 cm

• C.

26 cm

• D.

196 cm

• E.

256 cm

A. 14 cm
Explanation
Based on the given information, we can use the Law of Cosines to find the length of AB. The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the two sides and the cosine of the included angle. In this case, we have BC = 10 cm, AC = 16 cm, and ∠ACB = 60°. Plugging these values into the Law of Cosines, we get AB^2 = 10^2 + 16^2 - 2(10)(16)cos(60°). Simplifying this equation, we find AB^2 = 100 + 256 - 320(0.5) = 100 + 256 - 160 = 196. Taking the square root of both sides, we get AB = 14 cm. Therefore, the length of AB is 14 cm.

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• 17.

### Diketahui ∆ABC mempunyai panjang AB = 25  cm, BC = 25 cm, dan <BAC = 45º. Besar < BCA adalah ....

• A.

30º

• B.

45º

• C.

60º

• D.

105º

• E.

150º

C. 60º
Explanation
The given triangle ABC has two sides of equal length, AB and BC, which means it is an isosceles triangle. In an isosceles triangle, the angles opposite the equal sides are also equal. Therefore, since AB = BC, angle BCA is equal to angle BAC, which is given as 45º. Since the sum of all angles in a triangle is 180º, we can find the measure of angle BCA by subtracting the measures of angles BAC and BCA from 180º. Thus, angle BCA is 180º - 45º - 45º = 90º. However, the given options do not include 90º, so the closest option is 60º.

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• Current Version
• Mar 18, 2023
Quiz Edited by
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• May 25, 2017
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