smc-4552-20-cos

Trigonometry, SMB-022

Find the value of `theta`, correct to the nearest minute. (3 marks)

--- 5 WORK AREA LINES (style=lined) ---

Show Answers Only

`66^@ 25^{′}`

Show Worked Solution

`cos theta`	`=2/5`
`theta`	`=cos^{-1}(2/5)`
	`=66.421…^@`
	`=66^@ 25^{′} text{(to 1 d.p.)}`

Trigonometry, SMB-021

Express the ratio of `cos theta` in its simplest form. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---
Hence, find the value of `theta`, correct to two decimal places. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

`cos theta = 4/5`
`theta = 36.87^@`

Show Worked Solution

i. `text{By Pythagoras,}`

`x^2+8^2`	`=10^2`
`x^2`	`=100-36`
	`=64`
`x`	`=8`

`:.cos theta = 8/10=4/5`

ii. `theta`	`=cos^{-1}(4/5)`
	`=36.869…^@`
	`=36.87^@\ text{(to 2 d.p.)}`

Trigonometry, SMB-020

Find the value of `theta`, correct to the nearest minute. (2 marks)

Show Answers Only

`70^@ 32^{′}`

Show Worked Solution

`cos theta`	`=4/12`
`theta`	`=cos^{-1}(1/3)`
	`=70.528…`
	`=70^@ 31^{′}43^{″}`
	`=70^@ 32^{′}`

NOTE: Seconds > 30 are rounded up to the higher minute.

Trigonometry, SMB-019

Find the value of `theta`, correct to the nearest minute. (2 marks)

Show Answers Only

`54^@ 19^{′}`

Show Worked Solution

`cos theta`	`=7/12`
`theta`	`=cos^{-1}(7/12)`
	`=54.314…`
	`=54^@ 18^{′}52^{″}`
	`=54^@ 19^{′}`

Trigonometry, SMB-018

Find the value of `x`, correct to 1 decimal place. (2 marks)

Show Answers Only

`5.5`

Show Worked Solution

`cos 40^@`	`=4.2/x`
`x`	`=4.2/(cos 40^@)`
	`=5.5\ \ text{(to 1 d.p.)}`

Trigonometry, SMB-017

Find the value of `x`, correct to 2 decimal places. (2 marks)

Show Answers Only

`7.38`

Show Worked Solution

`cos 66^@`	`=3/x`
`x`	`=3/(cos 66^@)`
	`=7.38\ \ text{(to 2 d.p.)}`

Trigonometry, SMB-016

Find the value of `x`, correct to 2 decimal places. (2 marks)

Show Answers Only

`10.65`

Show Worked Solution

`cos 35^@`	`=x/13`
`x`	`=13 xx cos 35^@`
	`=10.65\ \ text{(to 2 d.p.)}`

Trigonometry, SMB-015

Find the value of `x`, correct to 2 decimal places. (2 marks)

Show Answers Only

`4.33`

Show Worked Solution

`cos 59^@`	`=x/8.4`
`x`	`=8.4 xx cos 59^@`
`x`	`=4.33\ \ text{(to 2 d.p.)}`

Trigonometry, SMB-014

Express `cos theta` as a fraction in its simplest form. (3 marks)

--- 6 WORK AREA LINES (style=lined) ---

Show Answers Only

`cos theta = sqrt3/2`

Show Worked Solution

`text{Let unknown side =}\ x`

`text{By Pythagoras:}`

`4^2`	`=x^2 + 2^2`
`x^2`	`=16-4`
`x`	`=sqrt12\ \ (x>0)`

`:.cos theta`	`=sqrt12/4`
	`= (2sqrt3)/4`
	`= sqrt3/2`

Trigonometry, SMB-013

Using Pythagoras and showing your working, express `cos 30^{@}` as a fraction. (2 marks)

--- 4 WORK AREA LINES (style=lined) ---

Show Answers Only

`cos 30^{@} = sqrt3/2`

Show Worked Solution

`text{Let}\ \ x =\ text{unknown side}`

`text{By Pythagoras:}`

`2^2`	`=x^2 + 1^2`
`x^2`	`=4-1`
`x`	`=sqrt3\ \ (x>0)`

`cos 30^{@} = text{adj}/text{hyp} = sqrt3/2`

Trigonometry, SMB-002

Express the following as a simplified fraction

`cos theta` (1 mark)

--- 1 WORK AREA LINES (style=lined) ---
`tan theta` (1 mark)

--- 1 WORK AREA LINES (style=lined) ---

Show Answers Only

`cos theta = 3/5`
`tan theta = 4/3`

Show Worked Solution

i. `cos theta = text{adj}/text{hyp} = 6/10 = 3/5`

ii. `tan theta = text{opp}/text{adj} = 8/6 = 4/3`

Measurement, STD2 M6 2009 HSC 4 MC

Which is the correct expression for the value of `x` in this triangle?

`8/cos30°`
`8/sin30°`
`8 xx cos30°`
`8 xx sin30°`

Show Answers Only

`A`

Show Worked Solution

`cos30^@`	`= 8/x`
`:.x`	`= 8/cos30^@`

`=> A`

Measurement, STD2 M6 2012 HSC 4 MC

Which expression could be used to calculate the value of `x` in this triangle?

`29 xx cos40^@`
`29 xx cos 50^@`
`cos40^@/29`
`cos50^@/29`

Show Answers Only

`A`

Show Worked Solution

♦ Mean mark 42%

`cos40^@`	`= x/29`
`x`	`= 29xxcos40^@`

`=> A`