Jeopardy

Radian Measure

100

π radian = ?

180°

200

convert each radian measure to degree 3π/6=?

3(180°)/=3(30°)=90°

300

what is radian?

the size of an angle that is subtended at the centre of a circle by an arc with a length equal to the radius of the circle a/r=r/r=1

400

π radians=180° π radians/π=?

180°/π=57.3％

500

convert each of the following angles to radians 1).30°

30°（π/180°）=π/6=0.52

Angle Formulas

100

sin(a)cos(b)-cos(a)sin(b)

Simplify sin(a-b)...

200

(√6−√2)/4

Determine the exact value if each trigonometric ratio. Cos(75°)=

300

sinx=cos(π/2 - x) =cos(π/2)cosx+sin(π/2)sinx = (0)(cosx)+(1)(sinx) =0+sinx =sinx

Use compound angle formulas to verify the following cofunction identities. sinx=cos(π/2 - x)

400

cosπ/3;1/2

Rewrite each expression as a single trigonometric ration, and then evaluate the ratio. cos5π/12 cosπ/12+sin5π/12 sinπ/12

500

Let C=x+y and letD= x-y. cosC-cosD =cos(x+y)-cos(x-y) =cosx cosy - sinx siny - (cosx cosy - sinx siny) =-2sinxsiny (c+d)/2=(x+y-x+y)/2=x (c-d)/2=(x+y-x+y)/2=y So cosC -cosD=-2sin((c+d)/2)sin((c+d)/2)

Prove cosc - cosd=-2sin((c+d)/2)sin((c-d)/2)

Transformation of trigonometric function

100

period π/2 amplitude 0.5 horizontal translation 0 equation of the axis y=0

Y=0.5cos(4x)

200

period π/2 amplitude 2 horizontal translation π/4 to the left equation of the axis y=4

Identify the key characteristics of Y=-2cos(4x+π)+4, and sketch its graph. Check your graph with a graphing calculator.

300

picture 3 300

Sketch each graph for 0≤x≤2π. Verify your sketch using graphing technology. Y=3sin(2(x-π/6))+1

400

reflection in the x-axis. horizontal stretch by a factor of 4

Sketch each graph for 0≤x≤2π. Verify your sketch using graphing technology. f(x)=sin（x-π）-1

500

Start with graph of y=sinx Reflect in the x-axis and stretch vertically by a factor of 2 to produce produce graph of y=-2sinx Translatπ/4 units to the right to produce graph of y=-2sin(0.5(x-π/4)) Tranlate 3units up to produce graph of y=-2sin(0.5(x-π/4))+3

Create a flow chart that summarises how you would use transformations to sketch the graph of f(x)=-2sin(0.5(x-π/4))+3

Proving Trigonometric Identities

100

A:=sinxcosy+cosxsiny B:=sinxcosy-cosxsiny

A:sin(x+y)= B:sin(x-y)=

200

LS=sin2x/1+cos2x =2sinxcosx/1+2cos²-1 =2sinxcosx/2cos²x =sinx/cosx =tanx=RS

Prove that sin2x/1+cos2x=tanx

300

LS=sinxcotx =(sinx)(cosx/sinx) =sinxcosx/sinx =cosx =RS

prove LS=RS sinxcotx=cosx

400

cos(2(π/3))=cos(2π/3)=-1/2 1+2sin²(π/3)=1+2*((√3)/2)² =1+6/4=10/4=5/2 not equal

Show this question is not an identity. cos2x=1+2sin²x

500

(cos²x-sin²x)/(cos²x+sinxcosx) =[(cosx-sinx)(cosx+sinx)]/[(cosx)(cosx+sinx)] =(cosx-sinx)/cosx =cosx/cosx-sinx/cosx =1-tanx

Prove this identity. (cos²x-sin²x)/(cos²x+sinxcosx)=1-tanx

formula

100

y=1/sinx y=1/cosx y=1/tanx

y=cscx=？ y=secx=? y=cotx=?

200

a=max-min/2

lal is the amplitude and a=?

300

3x+9x=5+7 12x=12 x=1

solve each equation to two decimal place where neccessary 3x-7=5-9x

400

true sin²=1-cos²x cos²x=1-sin²x

state whether each relationship is true or false

500

sinxcosy+cosxsiny cosxcosy-sinxsiny

sin(x+y)=? cos(x+y)?