Ch13 Trig ratio's and applications
In a triangle ABC, sin A = 1/8 , sin B = 3/4 and a = 5. Find, using the sine rule, the value of b.
30
Given that cos A = 1/3 where A is an acute angle, the value of cos(A/2) is:
SQRT(6)/3 or 0.8165
Convert the following polar coordinates into Cartesian coordinates:
(-2, pi)
(2,0)
Name a vector that is parallel to u = 3i+4j
Appropriate parallel vector
Define the Normal force
Force acting away and perpendicular from a surface
In a triangle ABC, a = 5, b = 6 and cos C =1/5 . Find the value of c.
7
If cos x = 3/5 and 0 < x < pi/2, then the exact value of sin x is:
4/5
Convert the following Cartesian coordinates into polar coordinates (-4, 4)
(4 SQRT(2), 3pi/4)
Find the scalar resolute of a in the direction of b if
a = 3i+2j, b= -i+4j
5
A rope is holding a 10kg weight to a ceiling. What is the tension force in the rope?
10kg wt
From a point on a cliff x m above sea level, the angle of depression to a boat is 30°. The distance from the foot of the cliff to the boat is 200 metres. Find the height of the cliff using exact values
200*SQRT(3) /3
The number of solutions of 2cos(3x) = 1, given that 0<x<pi is:
3
The graph of y=x^2 will intersect with its inverse graph at which coordinates?
(1, 1) and (-1,1)
If vector PQ= u, vector QR= v and vector RS= w, then vector SP is equal to:
-v-u-w
1 - Triangle of forces
2 - Resolution of forces
3 - Lami's theorem
A hiker travels a distance of 5 km from point P to point Q on a bearing of 030°. She then travels from point Q to point R on a bearing of 330° for 10 km. The distance west of R from P, in kilometres, is?
2.5
-cos x + sin x in the form r sin (x + a), where r > 0, is:
SQRT(2)*sin(x+7pi/4)
The radius length of the circle with equation x^2 - 12x + y^2 - 4y = 9 is:
7
Find the unit vector of a=5i+3j+4k
1/5*SQRT(2)(5i+3j+4k)
A force makes an angle of 40 degrees with the horizontal. If it's horizontal component is 10kg wt, with the magnitude of the force.
13.05kg wt
A vertical mast, AD, of height 20 m is supported by two cables attached to the ground at two points C and B. Angle(CAB) is a right angle. Cable CD is of length 40 m and cable BD is of length 30 m.
The angle ABC, to the nearest degree, is:
57 degrees
Prove the following
a sin 2x = 2tanx/(1+tan^2(x))
Successful proof
Describe graph of the of locus of points P(x, y) such that that PA + PB = 5 given coordinates A(3, 0) and B(-1, 0).
an ellipse with centre (1, 0)
Find the vector resolute of a = 3i+4j in the direction of b = -8i + 6j
Zero vector
A 10 kg weight is resting on a smooth plane inclined at 30° to the horizontal and is prevented from slipping down the plane by a string parallel to the plane The magnitude of N is approximately:
8.66 kg wt