IB Math SL Year 2Name: ________________________Date: _________________________

5-5 Graphing Tangent and PracticeLearning Goal: How do we graph Sine and Cosine Curves?

Critical Values for y = Sin(x)

Critical Values for y = Cos(x)

Now you Try! Critical Values for y = Tan(x)

Degrees -360˚ -270˚ -180˚ -90˚ 0˚ 90˚ 180˚ 270˚ 360˚

Radians -2-

3 π2 -

-

π2 0

π2

3 π2

2

Tan θ

*We will revisit the graph of Tan(x) whenwe move into solving equations!

Degrees

-360˚ -270˚ -180˚ -90˚ 0˚ 90˚ 180˚ 270˚

360˚

Radians -2-

3 π2 -

-

π2 0

π2

3 π2

2

Sin θ

Degrees

-360˚ -270˚ -180˚ -90˚ 0˚ 90˚ 180˚ 270˚

360˚

Radians -2-

3 π2 -

-

π2 0

π2

3 π2

2

Cos θ

IB Math SL Year 2Mixed Practice

1. The diagram shows the graph of the function f given by

f (x) = A sin

x

2

+ B, for 0 x 5, where A and B are constants, and x is measured in radians.

0 1 2 3 4 5

2

y

x(0 , 1 )

(1 ,3 )

(3 , – 1 )

(5 , 3 )

The graph includes the points (1, 3) and (5, 3), which are maximum points of the graph.

(a) Write down the values of f (1) and f (5).

(b) Show that the period of f is 4.

The point (3, –1) is a minimum point of the graph.

(c) Show that A = 2, and find the value of B.

2.

IB Math SL Year 23.

4. The diagram below shows a circle of radius 5 cm with centre O. Points A and B are on the circle, and BOA is 0.8 radians. The point N is on [OB] such that [AN] is perpendicular to [OB]. Find the area of the shaded region.

0 .8

5 cm

N

A

BO

IB Math SL Year 25. The diagram below shows a circle, centre O, with a radius 12 cm.

The chord AB subtends at an angle of 75° at the centre. The tangents to the circle at A and at B meet at P.

(a) Using the cosine rule, show that the length of AB is

12 75cos–12 .

(b) Find the length of BP.

(c) Hence find

(i) the area of triangle ABP;

(ii) the area of triangle OBP.

(d) Find the area of sector OAB.

(e) Find the area of the shaded region.

1 2 cmA

P

B

75 ºO d ia gram n o t tosca le

Hint: set up cosine rule and pull out a GCF.

Hint: Redraw quadrilateral AOPB.

Radii perpendicular to tangent segments (AB and BP)

All Angles in a triangle add to 180; Isosceles triangles have 2 congruent base angles.

Hint: Hint:Area of shaded = Area of Quadrilateral – A(sector)

Area(quadrilateral) = 2*A(Triangle OBP)

IB Question

IB Math SL Year 26. A nautical mile (nmi) is the distance on the Earth’s surface that subtends an angle of 1

minute (or 160 of a degree) of the Great Circle arc measured from the centre of the

Earth.

A knot is a speed of 1 nautical mile per hour.

a) Given that the radius of the Earth is 6370km, show that 1 nmi is approximately equal to 1.853 km.

b) Calculate how long it would take a plan to fly from Perth to Adelaide (a distance of 2130km) if the plane can fly at 480 knots.

Hints:

1) How many nmi are we traveling?2) If 1 knot = 1nmi/hr, then 450 knots = ?

IB Math SL Year 2