Asked by Maggie.K

1)Solve the equation: sin(2x+10)°=√3/2 for 0°<or=x<or=360°
2)Solve for x in the equation:sin[5/2x]°=-1/2 for 0°<or=x<or<or=360°
3)Solve for x in the equation; tan x=2sin x for -180°<or=x<or=180°
4)Find the value of x in the equation; cos(3x+180)°=√3/2 for 0°<or=x<or=180°
5)Solve for titre in the equation; -1/4sin(2titre+30)°=0.1607 for 0°<or= x<or=360°
6)Given that cos a=5/13 and that 270°<or=a<or=360°,evaluate tan a+sin a
7)If tan titre=12/5 and titre is reflex,find the value of 5sin titre+cos titre
8)Find titre given that 2cos3titre-1=0 for 0°<or=x<or=360°
9)Solve the equation; 2cos2(x+30)°=-1 for 0°<or=x<or=360°
10)Solve for titre in the equation; cos(2titre+30)=-0.7660 for -180°<or=x<or=180°
11)Solve the equation 2 tan 2xcos2x+√3=0 for -180°<or=x<or=180°
12)Given that 3tan^2(2x+2/3π°=1,Find x when 0°<or=x<or=2π°.Give your answer in π°
13)A figure has point D which divides AC in the ratio 1:1.AB=6.4cm, angle ABD=39° and angle BAD=78°.Calculate correct to 1 d.p;
a)The length of BD
b)The length of BC
14)A triangle ABC is inscribed in a circle.AB=6cm.BC=9cm and angle ABC=80°.Calculate to one decimal place;
a)The length of AC
b)The radius of the circle
c)The area of the shaded segments


Answers

There are no human answers yet.
Answered by GPT 3.5
1) To solve the equation sin(2x+10)° = √3/2 for 0° ≤ x ≤ 360°, we need to find the values of x that make the equation true.

First, consider when sin(2x+10)° = √3/2. This occurs when the angle (2x+10)° is equal to π/3 or 60°.

Now we can set up an equation: 2x + 10 = 60.

Subtracting 10 from both sides gives us: 2x = 50.

Dividing both sides by 2 gives us: x = 25.

So the solution to the equation is x = 25.

2) To solve the equation sin(5/2x)° = -1/2 for 0° ≤ x ≤ 360°, we need to find the values of x that make the equation true.

First, consider when sin(5/2x)° = -1/2. This occurs when the angle (5/2x)° is equal to -π/6 or -30°.

Now we can set up an equation: 5/2x = -30.

Multiplying both sides by 2/5 gives us: x = -12.

So the solution to the equation is x = -12.

3) To solve the equation tan(x)=2sin(x) for -180° ≤ x ≤ 180°, we need to find the values of x that make the equation true.

First, we can rewrite tan(x) as sin(x)/cos(x). Now the equation becomes sin(x)/cos(x) = 2sin(x).

Multiplying both sides by cos(x) gives us: sin(x) = 2sin(x)cos(x).

Dividing both sides by sin(x) gives us: 1 = 2cos(x).

Dividing both sides by 2 gives us: 1/2 = cos(x).

So the solution to the equation is x = 60°.

4) To solve the equation cos(3x+180)° = √3/2 for 0° ≤ x ≤ 180°, we need to find the values of x that make the equation true.

First, consider when cos(3x+180)° = √3/2. This occurs when the angle (3x+180)° is equal to π/6 or 30°.

Now we can set up an equation: 3x + 180 = 30.

Subtracting 180 from both sides gives us: 3x = -150.

Dividing both sides by 3 gives us: x = -50.

So the solution to the equation is x = -50.

5) To solve the equation -1/4sin(2t+30)° = 0.1607 for 0° ≤ t ≤ 360°, we need to find the values of t that make the equation true.

First, consider when -1/4sin(2t+30)° = 0.1607. This occurs when the angle (2t+30)° is equal to sin^(-1)(-0.1607) or -9.209°.

Now we can set up an equation: 2t + 30 = -9.209.

Subtracting 30 from both sides gives us: 2t = -39.209.

Dividing both sides by 2 gives us: t = -19.6045.

So the solution to the equation is t = -19.6045.

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